The DOI matches its Crossref record; 20 of the 46 references it cites were found in a registry or an index, and 26 are not checked yet; none of the 35 sources its claims cite is checked for support yet.
Unifying time evolution and optimization with matrix product states
Open accessAbstract
We show that the time-dependent variational principle provides a unifying framework for time-evolution methods and optimization methods in the context of matrix product states. In particular, we introduce a new integration scheme for studying time evolution, which can cope with arbitrary Hamiltonians, including those with long-range interactions. Rather than a Suzuki-Trotter splitting of the Hamiltonian, which is the idea behind the adaptive time-dependent density matrix renormalization group method or time-evolving block decimation, our method is based on splitting the projector onto the matrix product state tangent space as it appears in the Dirac-Frenkel time-dependent variational principle. We discuss how the resulting algorithm resembles the density matrix renormalization group (DMRG) algorithm for finding ground states so closely that it can be implemented by changing just a few lines of code and it inherits the same stability and efficiency. In particular, our method is compatible with any Hamiltonian for which ground-state DMRG can be implemented efficiently. In fact, DMRG is obtained as a special case of our scheme for imaginary time evolution with infinite time step.
Checked 2026-10-05 · 26 references not checked yet
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
0 of 35 cited sources checked · 0 supported · 0 flagged
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Without truncation (ε = 0), one can easily verify that, after applying the complete sweep (left-to-right and back) with a time step t to an MPS | [A] , the original physical state | [A] is obtained by reapplying the scheme with a time stept, although | [A] will now be encoded as an MPS with a larger bond dimension (and matrices l(n) or r(n), which do not have full rank).”
§ Unifying time evolution and optimization with matrix product states > APPENDIX C: DERIVATION OF THE TWO-SITE INTEGRATION SCHEME
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“That the adjoint method for the finite MPS integrator can be evaluated explicitly can be traced back to the fact that the individual terms obtained from splitting the tangent space projector are exactly integrable.”
§ Unifying time evolution and optimization with matrix product states > APPENDIX B: FULL ALGORITHM FOR THE SYMMETRIC ONE-SITE INTEGRATOR
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“That these two gauge fixing conditions are related to a principal bundle connection implies that they transform covariantly under gauge transformations on the original MPS.”
§ Unifying time evolution and optimization with matrix product states > VII. CONCLUSIONS
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“This ensures that the overlap of two tangent vectors only contains diagonal contributions, as in [B 1 ]| [B 2 ] = N n=1 s n tr B s n 1 (n) † B s n 2 (n) .(A8) This corresponds to the standard Euclidean inner product and thus to the choice of an orthonormal basis.”
§ Unifying time evolution and optimization with matrix product states > VII. CONCLUSIONS
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“If the original MPS was already in the right canonical form, the singular values of C(n) correspond to the Schmidt coefficients of | for a bipartition of the lattice in [1 : n] and [n + 1 : N ].”
§ Unifying time evolution and optimization with matrix product states > APPENDIX C: DERIVATION OF THE TWO-SITE INTEGRATION SCHEME
Strength:plain· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“As for the tangent space, the linear map from the representation {B s,t (n : n + 1); n = 1, . . .,N -1} to the physical states in T [2] | [A] M MPS has a nontrivial kernel corresponding to choices B s,t (n : n + 1) = A s L (n)X t (n + 1) -X s (n)A t R (n + 1) for any {X(n) ∈ C D n ×d×D n+1 ,n = 2, . . .,N -1}.”
§ Unifying time evolution and optimization with matrix product states > APPENDIX C: DERIVATION OF THE TWO-SITE INTEGRATION SCHEME
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“That the adjoint method for the finite MPS integrator can be evaluated explicitly can be traced back to the fact that the individual terms obtained from splitting the tangent space projector are exactly integrable.”
§ Unifying time evolution and optimization with matrix product states > APPENDIX B: FULL ALGORITHM FOR THE SYMMETRIC ONE-SITE INTEGRATOR
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“This freedom allows to impose a gauge-fixing condition of the form s A s L (n) † B s,t (n : n + 1) = 0, ∀n = 1, . . .,N -2.(C2)”
§ Unifying time evolution and optimization with matrix product states > APPENDIX C: DERIVATION OF THE TWO-SITE INTEGRATION SCHEME
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Inserting this solution into | [B] gives immediate rise to | [B] = P T | [A] M MPS | = N n=1 P [1:n-1] L ⊗ 1n ⊗ P [n+1:N] R - N-1 n=1 P [1:n] L ⊗ P [n+1:N] R | ,(A12) where we can recognize the contents of the brackets as the decomposition of the tangent space projector into a sum of orthogonal projectors”
§ Unifying time evolution and optimization with matrix product states > VII. CONCLUSIONS
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In the case of a nearest-neighbor Hamiltonian, the projector error is absent as the action of Ĥ on | [A] is exactly contained in T [2] | [A L ] M MPS .”
§ Unifying time evolution and optimization with matrix product states > APPENDIX C: DERIVATION OF THE TWO-SITE INTEGRATION SCHEME
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
- It may state two separate claims as one. 29
- Probably not a substantial claim. 12
- The quote only partly states this claim. 1
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The solution to this constrained optimization problem is given by B s (n) = t (δ s,t -A s L (n)A t L (n) † )F t (n) for all n = 1, . . .,N -1, where first factor is a projector that imposes the left-gauge fixing condition.Tensor B(N ) is not subject to any constraint and is given by B s (N ) = F s (N ).”
§ Unifying time evolution and optimization with matrix product states > VII. CONCLUSIONS
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In particular, by directly applying a nearest-neighbor Hamiltonian Ĥ = N-1 n=1 ĥ(n : n + 1) to | [A] , one obtains a state of the form of Eq. (C1), which is represented by B s 1 ,s 2 (n : n + 1) = t 1 ,t 2 s 1 ,s 2 | ĥ(n : n + 1)|t 1 ,t 2 A s 1 (n)A s 2 (n).This is different from the representation in Eq. (C4), even though both describe the same physical state Ĥ | [A] .”
§ Unifying time evolution and optimization with matrix product states > APPENDIX C: DERIVATION OF THE TWO-SITE INTEGRATION SCHEME
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
In the paper
“For α > 1, we observe a light cone and the leakage outside is in perfect agreement with the theoretical predictions of Ref. [38].”
§ Unifying time evolution and optimization with matrix product states > VI. EXAMPLE
What the sources say
- Not checked yetcites [38] source
Strength:boosted· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The resulting virtual dimensions of the MPO are 28, 28, 24, and 12 for the cases α = 0.75, 1.5, 3.0 and 6.0, respectively.”
§ Unifying time evolution and optimization with matrix product states > VI. EXAMPLE
Strength:plain· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The light cone itself seems to be linear for α = 3.0 and α = 6.0, but the shape is less clear for α = 1.5.”
§ Unifying time evolution and optimization with matrix product states > VI. EXAMPLE
Strength:hedged· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Absolute value of 0 |U † σ x r (t)U | 0 -0 |σ x r (t)| 0 with H the XY Hamiltonian in Eq. (9), | 0 the ground state of H and U = exp(iσ y 51 π/4) on a chain of N = 101 spins, as function of r and t for various values of α.”
§ Unifying time evolution and optimization with matrix product states > APPENDIX C: DERIVATION OF THE TWO-SITE INTEGRATION SCHEME
Strength:plain· not yet calibratedn = 101Tests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“For α = 0.75, there is no sharp wave front but it still seems to take a finite amount of time to signal over a finite distance, up to power law corrections.”
§ Unifying time evolution and optimization with matrix product states > VI. EXAMPLE
Strength:hedged· not yet calibratedSingle caseTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The underlying reason for this is that the effective Hamiltonian H (n) [or C(n)] for the one-site [or zero-site] center degrees of freedom A C (n) [or C(n)] does not depend on these degrees of freedom, but only on the tensors on the neighboring sites, so that the differential equations corresponding to the individual terms are first-order linear differential equations.”
§ Unifying time evolution and optimization with matrix product states > APPENDIX B: FULL ALGORITHM FOR THE SYMMETRIC ONE-SITE INTEGRATOR
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We furthermore relate this two-site approach to the more conventional time-dependent DMRG or TEBD methods, which are restricted to local (typically nearestneighbor) interactions.”
§ Unifying time evolution and optimization with matrix product states > I. INTRODUCTION
Strength:plain· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“By construction, the resulting evolution will never leave the MPS manifold and can therefore be described by time-evolving parameters as | (A(t)) .”
§ Unifying time evolution and optimization with matrix product states > III. TANGENT SPACE PROJECTOR AND TIME-DEPENDENT VARIATIONAL PRINCIPLE
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“By construction, the TDVP projects the evolution onto the manifold of MPS with fixed bond dimension and avoids the need for a truncation step.”
§ Unifying time evolution and optimization with matrix product states > I. INTRODUCTION
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We discuss how the resulting algorithm resembles the density matrix renormalization group (DMRG) algorithm for finding ground states so closely that it can be implemented by changing just a few lines of code and it inherits the same stability and efficiency.”
§ Unifying time evolution and optimization with matrix product states > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Indeed, the TDVP can be recast into a complicated set of coupled nonlinear equations for all parameters in the MPS.”
§ Unifying time evolution and optimization with matrix product states > III. TANGENT SPACE PROJECTOR AND TIME-DEPENDENT VARIATIONAL PRINCIPLE
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“For this type of differential equation consisting of a sum of integrable parts, it is very natural to use a Lie-Trotter splitting approach [16,29,30], where one evolves according to each integrable part for a small time t.”
§ Unifying time evolution and optimization with matrix product states > ONE-SITE INTEGRATION SCHEME
What the sources say
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
In the paper
“The algorithm presented in Ref. [18] used the explicit Euler integration scheme to simultaneously update all parameters, which was only possible by using explicit inverses of matrices containing very small singular values.”
§ Unifying time evolution and optimization with matrix product states > III. TANGENT SPACE PROJECTOR AND TIME-DEPENDENT VARIATIONAL PRINCIPLE
What the sources say
- Not checked yetcites [18] source
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“As explained in Ref. [29], this source of error can be bound in terms of ( 1 -PT | [A] M MPS ) Ĥ | [A] , a quantity that can easily be evaluated [33] and monitored throughout the evolution.”
§ Unifying time evolution and optimization with matrix product states > ONE-SITE INTEGRATION SCHEME
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
In the paper
“Having a Lanczos routine for computing the matrix exponential acting on a vector (e.g., Ref. [31]), this algorithm differs from one-site DMRG by replacing the optimization step for A C (n) (eigenvalue solver) with the evolution step, and by adding an extra evolution step for C(n) before absorbing it at the next site.”
§ Unifying time evolution and optimization with matrix product states > ONE-SITE INTEGRATION SCHEME
What the sources say
- Not checked yetcites [31] source
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
In the paper
“The individual optimization steps are homogeneous problems and give rise to a generalized eigenvalue equation.”
§ Unifying time evolution and optimization with matrix product states > II. MATRIX PRODUCT STATES AND CANONICAL FORMS
What the sources say
- Not checked yetcites [15] source
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“For example, using the single projector P [1:n-1] L ⊗ 1n ⊗ P [n+1:N] R and writing | [A] as in Eq. ( 1) with center site n, the exact solution can be obtained by only making A C (n) timedependent and letting it satisfy ȦC (n,t) = -iH (n) A C (n,t) where a bold notation is used for the vector representation of A C (n).”
§ Unifying time evolution and optimization with matrix product states > ONE-SITE INTEGRATION SCHEME
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
In the paper
“Analogous to the eigenvalue problem in DMRG, both Eqs. ( 7) and ( 8) can be integrated using a Lanczos scheme [28] in order to keep the computational cost at O(D 3 ).”
§ Unifying time evolution and optimization with matrix product states > ONE-SITE INTEGRATION SCHEME
What the sources say
- Not checked yetcites [28] source
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The resulting algorithm resembles DMRG so closely that it can be obtained by merely modifying two lines of code, and the one-site DMRG method is obtained as special case of imaginary time evolution with an infinite time step.”
§ Unifying time evolution and optimization with matrix product states > I. INTRODUCTION
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This approach is independent of the Hamiltonian and can be implemented efficiently for long-range Hamiltonians.”
§ Unifying time evolution and optimization with matrix product states > I. INTRODUCTION
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
In the paper
“There is a natural order similar to the DRMG sweep, which optimizes the computational overhead (and results in robustness in the case of overapproximation [27]).”
§ Unifying time evolution and optimization with matrix product states > ONE-SITE INTEGRATION SCHEME
What the sources say
- Not checked yetcites [27] source
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
In the paper
“Completing the right-to-left sweep is equivalent to composing this integrator with its adjoint, resulting in a second-order symmetric method [32] so that the state at time t + 2 t has a more favourable error of order O( t 3 ).”
§ Unifying time evolution and optimization with matrix product states > ONE-SITE INTEGRATION SCHEME
What the sources say
- Not checked yetcites [32] source
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The evolution of C in Eq. ( 8) can be interpreted as an evolution backwards in time.”
§ Unifying time evolution and optimization with matrix product states > ONE-SITE INTEGRATION SCHEME
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesThe quote only partly states this claim.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“These operators are independent of the unitary gauge freedom (basis rotation) that exists in the definition of | [1:n] L,α and | [n:N] R,β and correspond to orthogonal projectors onto the support of the reduced density matrix ρ of the state | [A] in the corresponding regions.”
§ Unifying time evolution and optimization with matrix product states > III. TANGENT SPACE PROJECTOR AND TIME-DEPENDENT VARIATIONAL PRINCIPLE
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“While K(n) serves no purpose in ground-state DMRG, it will appear in our time evolution algorithm below.”
§ Unifying time evolution and optimization with matrix product states > FIG. 2. (a)
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“An alternative idea for time evolution, the Dirac-Frenkel time-dependent variational principle (TDVP), was formulated only recently for the variational class of MPS [18,19].”
§ Unifying time evolution and optimization with matrix product states > I. INTRODUCTION
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This allows to dynamically adapt the bond dimension to the a predefined precision or error criterion, and also allows to dynamically introduce new charge sectors (irreducible representations) when symmetries of the quantum state are explicitly encoded in the MPS representation.”
§ Unifying time evolution and optimization with matrix product states > V. TWO-SITE ALGORITHM
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
In the paper
“In Ref. [38], the time-dependent expectation value σ x r (t) = exp(-iH t)σ x r exp(iH t) was compared between a fully polarized product state | 0 = ⊗ n |↑ n and the perturbed state U | 0 with U = exp(iπσ y 0 /4) as function of r and t for various values α > 1.”
§ Unifying time evolution and optimization with matrix product states > VI. EXAMPLE
What the sources say
- Not checked yetcites [38] source
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The representation B s n ,s n+1 (n : n + 1) is, however, nonunique, and our algorithm based on splitting the projector (even when it acts trivially) gives rise to a slightly different scheme.”
§ Unifying time evolution and optimization with matrix product states > V. TWO-SITE ALGORITHM
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
In the paper
“As two MPS with different bond dimensions do not belong to the same manifold [35], this idea cannot easily be captured in a smooth evolution described using a differential equation.”
§ Unifying time evolution and optimization with matrix product states > V. TWO-SITE ALGORITHM
What the sources say
- Not checked yetcites [35] source
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This result justifies the two-site integration scheme that was proposed in the main text.”
§ Unifying time evolution and optimization with matrix product states > APPENDIX C: DERIVATION OF THE TWO-SITE INTEGRATION SCHEME
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
In the paper
“In accordance with the general result of that paper, there is a light cone and the leakage outside the light cone contains a contribution with exponential decay that is determined by the nearest-neighbor interactions and is thus independent of α, as well as a contribution with power-law decay that dominates at larger distances.”
§ Unifying time evolution and optimization with matrix product states > VI. EXAMPLE
What the sources say
- Not checked yetcites [38] source
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
In the paper
“This Hamiltonian was recently realized in an experiment with trapped 171 Yb + ions [39].”
§ Unifying time evolution and optimization with matrix product states > VI. EXAMPLE
What the sources say
- Not checked yetcites [39] source
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Finding a unique parametrization for every tangent vector is equivalent to specifying a complement of the vertical subspace (the so-called horizontal subspace), for which there is no unique prescription.”
§ Unifying time evolution and optimization with matrix product states > VII. CONCLUSIONS
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This approach generalizes neatly to tree tensor network states and will be equally relevant for continuous MPS [24,25], where algorithms based on a Trotter decomposition of the Hamiltonian terms are not applicable.”
§ Unifying time evolution and optimization with matrix product states > VII. CONCLUSIONS
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Hence, without the truncation, the integrator is still symmetric and one expects a finite time step error that scales as O( t 3 ).”
§ Unifying time evolution and optimization with matrix product states > APPENDIX C: DERIVATION OF THE TWO-SITE INTEGRATION SCHEME
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“One can easily verify that the C(n) that results from then factorizing A C (n) = A L (n)C(n) is then also an exact eigenstate of K(n), so that its backwards evolution has no further effect and can thus be omitted.”
§ Unifying time evolution and optimization with matrix product states > ONE-SITE INTEGRATION SCHEME
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
In the paper
“For this choice of | 0 , the quantum many-body problem can be reduced to a single-particle problem.”
§ Unifying time evolution and optimization with matrix product states > VI. EXAMPLE
What the sources say
- Not checked yetcites [38] source
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The tangent space projector is a generic concept that is independent of the TDVP and can be applied to arbitrary states | in the Hilbert space H.”
§ Unifying time evolution and optimization with matrix product states > APPENDIX C: DERIVATION OF THE TWO-SITE INTEGRATION SCHEME
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes? Based: unclearIt may state two separate claims as one.
The paper relies on this without support.
The TEBD idea cannot be applied to long-range interactions.
“Unfortunately, the TEBD idea is not applicable to long-range interactions, which appear when using MPS for quasi-2D systems or quantum chemistry applications.”
The authors state this as an assumption.
The truncation scheme discards singular values smaller than a tolerance level ε.
“For the remainder, we assume that the truncation scheme is based on discarding singular values smaller than some tolerance level ε.”
The paper relies on this without support.
The set of MPS with all possible bond dimensions constitutes a stratification.
“The set of MPS with all possible bond dimensions constitutes a stratification .”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“In Ref. [20] a slightly different error was proposed that avoids this numerical inaccuracy.”
From Tangent-space methods for uniform matrix product states (2019) · cites this paper as [20]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Two-site gauge tensor dimensions are shifted by one site
MinorThe stated dimensions for X(n) match a tensor at site n + 1, but the displayed expression uses X(n) at site n. Under the paper's site-tensor dimensions, X(n) would need dimensions D n-1 × d × D n for that expression to be compatible.
“B s,t (n : n + 1) = A s L (n)X t (n + 1) -X s (n)A t R (n + 1) for any {X(n) ∈ C D n ×d×D n+1 ,n = 2, . . .,N -1}.”
“A s (n) having site-dependent dimensions D n-1 × D n .”
Reverse sweep gives the new center two different site indices
MinorStep 3(c) says absorbing the bond tensor into the tensor at site n produces a center at n + 1. Step 3(d) instead uses the resulting center at site n.
“(c) Absorb C(n,t + t/2) into A L (n,t + t/2) to obtain A C (n + 1,t + t/2).”
“(d) Evolve A C (n,t + t/2) forward in time according to A C (n,t + t) = exp[-iH (n) t/2] A C (n,t + t/2)”
Reverse sweep assigns the right-hand tensor to the wrong site
MinorStep 3(a) decomposes a center tensor at site n + 1 but labels the resulting right-hand tensor as being at site n. The following step uses a right-hand tensor at site n + 1 instead.
“(a) Perform an orthogonal decomposition of A C (n + 1,t + t) into C(n,t + t) and A R (n,t + t).”
“where K(n) is computed using A L (1,t + t/2),...,A L (n,t + t/2), A R (n + 1,t + t), ..., A R (N,t + t).”
Citations
Cites
Density matrix formulation for quantum renormalization groups
White, S. R. (1992) · Physical Review Letters · doi:10.1103/physrevlett.69.2863 · Cited by 7,702
The density-matrix renormalization group in the age of matrix product states
Schollwöck, U. (2011) · Annals of Physics · doi:10.1016/j.aop.2010.09.012 · Cited by 4,818
Solving Ordinary Differential Equations II
Hairer, E., & Wanner, G. (1996) · Springer Series in Computational Mathematics · doi:10.1007/978-3-642-05221-7 · Cited by 4,342
Density-matrix algorithms for quantum renormalization groups
White, S. R. (1993) · Physical Review B · doi:10.1103/physrevb.48.10345 · Cited by 3,244
Oseledets, I. V. (2011) · SIAM Journal on Scientific Computing · doi:10.1137/090752286 · Cited by 2,860
Self-citationCompletely positive linear maps on complex matrices
Choi, M.-D. (1975) · Linear Algebra and its Applications · doi:10.1016/0024-3795(75)90075-0 · Cited by 2,659
On the product of semi-groups of operators
Trotter, H. F. (1959) · Proceedings of the American Mathematical Society · doi:10.1090/s0002-9939-1959-0108732-6 · Cited by 2,282
Verstraete, F., Murg, V., & Cirac, J. I. (2008) · Advances In Physics · doi:10.1080/14789940801912366 · Cited by 1,841
Self-citationEfficient Simulation of One-Dimensional Quantum Many-Body Systems
Vidal, G. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.040502 · Cited by 1,779
Linear transformations which preserve trace and positive semidefiniteness of operators
Jamiołkowski, A. (1972) · Reports on Mathematical Physics · doi:10.1016/0034-4877(72)90011-0 · Cited by 1,512
Flagged first, then by citations
Cited by
Sorted by citations
Items 301–400 of 803
Interaction-driven dynamical quantum phase transitions in a strongly correlated bosonic system
Stumper, S., Thoss, M., & Okamoto, J. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.013002 · Cited by 16
BaOsO3 : A Hund's metal in the presence of strong spin-orbit coupling
Bramberger, M., Mravlje, J., Grundner, M., Schollwöck, U., & Zingl, M. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.103.165133 · Cited by 16
Characterizing the quantum field theory vacuum using temporal Matrix Product statesPreprint
Tirrito, E., Robinson, N. J., Lewenstein, M., Ran, S.-J., & Tagliacozzo, L. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1810.08050 · Cited by 16
Realization of a Rydberg-dressed extended Bose-Hubbard model
Weckesser, P., Srakaew, K., Blatz, T., Wei, D., Adler, D., Agrawal, S., Bohrdt, A., Bloch, I., & Zeiher, J. (2025) · Science · doi:10.1126/science.adq7082 · Cited by 29
Nonstabilizerness Dynamics in Many-Body Localized Systems
Falcão, P. R. N., Sierant, P., Zakrzewski, J., & Tirrito, E. (2025) · Physical Review Letters · doi:10.1103/xfp5-hhs4 · Cited by 15
Ke, Y., Dvořák, J., Čížek, M., Borrelli, R., & Thoss, M. (2023) · The Journal of Chemical Physics · doi:10.1063/5.0155290 · Cited by 15
Quantifying Rare Events in Stochastic Reaction-Diffusion Dynamics Using Tensor Networks
Nicholson, S. B., & Gingrich, T. R. (2023) · Physical Review X · doi:10.1103/physrevx.13.041006 · Cited by 15
Environmentally Driven Symmetry Breaking Quenches Dual Fluorescence in Proflavine
Hunter, K. E., Mao, Y., Chin, A. W., & Zuehlsdorff, T. J. (2024) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.4c00677 · Cited by 15
Large-scale 2 + 1D U(1) gauge theory with dynamical matter in a cold-atom quantum simulator
Osborne, J. J., McCulloch, I. P., Yang, B., Hauke, P., & Halimeh, J. C. (2025) · Communications Physics · doi:10.1038/s42005-025-02144-8 · Cited by 15
Wu, Y. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.101.064427 · Cited by 15
Dunnett, A., & Chin, A. W. (2021) · Entropy · doi:10.3390/e23010077 · Cited by 18
Using tensor network states for multi-particle Brownian ratchets
Strand, N. E., Vroylandt, H., & Gingrich, T. R. (2022) · The Journal of Chemical Physics · doi:10.1063/5.0097332 · Cited by 15
Ge, Y., Li, W., Ren, J., & Shuai, Z. (2022) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.2c00651 · Cited by 15
DYNAMICS, NUMERICAL ANALYSIS, AND SOME GEOMETRY
Gauckler, L. J., Hairer, E., & Lubich, C. (2019) · International Congress of Mathematicians (ICM) · doi:10.1142/9789813272880_0020 · Cited by 17
Self-citationTheory of Metastable States in Many-Body Quantum Systems
Yin, C., Surace, F. M., & Lucas, A. (2025) · Physical Review X · doi:10.1103/physrevx.15.011064 · Cited by 14
Garcia, J. S., & Chepiga, N. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.110.125113 · Cited by 14
Quantum many-body scars from unstable periodic orbits
Evrard, B., Pizzi, A., Mistakidis, S. I., & Dağ, C. B. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.110.144302 · Cited by 14
Local ergotropy and its fluctuations across a dissipative quantum phase transition
Bello, G. D., Farina, D., Jansen, D. J., Perroni, C. A., Cataudella, V., & Filippis, G. D. (2024) · Quantum Science and Technology · doi:10.1088/2058-9565/ad9cbb · Cited by 14
Approximate Quantum Compiling for Quantum Simulation: A Tensor Network Based Approach
Robertson, N., Akhriev, A., Vala, J., & Zhuk, S. M. (2025) · ACM Transactions on Quantum Computing · doi:10.1145/3731251 · Cited by 14
Probing critical phenomena in open quantum systems using atom arrays
Fang, F., Wang, K., Liu, V. S., Wang, Y., Cimmino, R., Wei, J., Bintz, M., Parr, A., Kemp, J., Ni, K.-K., et al. (2025) · Science · doi:10.1126/science.adq0278 · Cited by 30
Entanglement of Formation of Mixed Many-Body Quantum States via Tree Tensor Operators
Arceci, L., Silvi, P., & Montangero, S. (2022) · Physical Review Letters · doi:10.1103/physrevlett.128.040501 · Cited by 15
Quantum dynamics of vibrational energy flow in oscillator chains driven by anharmonic interactions
Borrelli, R., & Gelin, M. F. (2020) · New Journal of Physics · doi:10.1088/1367-2630/abc9ed · Cited by 14
Dynamics of many-body delocalization in the time-dependent Hartree–Fock approximation
Pöpperl, P., Doggen, E. V. H., Karcher, J. F., Mirlin, A. D., & Tikhonov, K. S. (2021) · Annals of Physics · doi:10.1016/j.aop.2021.168486 · Cited by 14
Dual current anomalies and quantum transport within extended reservoir simulations
Wójtowicz, G., Elenewski, J. E., Rams, M. M., & Zwolak, M. P. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.104.165131 · Cited by 14
Ren, J., Wang, Y.-H., Li, W., Jiang, T., & Shuai, Z. (2021) · Chinese Journal of Chemical Physics · doi:10.1063/1674-0068/cjcp2108138 · Cited by 14
Achieving the quantum field theory limit in far-from-equilibrium quantum link models
Halimeh, J. C., Damme, M. V., Zache, T. V., Banerjee, D., & Hauke, P. (2022) · Quantum · doi:10.22331/q-2022-12-19-878 · Cited by 23
Lattice control of nonergodicity in a polar lattice gas
Korbmacher, H., Sierant, P., Li, W., Deng, X., Zakrzewski, J., & Santos, L. (2023) · Physical Review A · doi:10.1103/physreva.107.013301 · Cited by 14
Stable bipolarons in open quantum systems
Moroder, M., Grundner, M., Damanet, F., Schollwöck, U., Mardazad, S., Flannigan, S., Köhler, T., & Paeckel, S. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.107.214310 · Cited by 16
Gonzalez-Ballestero, C., Schröder, F. A. Y. N., & Chin, A. W. (2017) · Physical review. B./Physical review. B · doi:10.1103/physrevb.96.115427 · Cited by 14
Density of states of many-body quantum systems from tensor networks
Schrodi, F., Silvi, P., Tschirsich, F., Fazio, R., & Montangero, S. (2017) · Physical review. B./Physical review. B · doi:10.1103/physrevb.96.094303 · Cited by 14
Fast time evolution of matrix product states using the QR decomposition
Unfried, J., Hauschild, J., & Pollmann, F. (2023) · Physical Review B · doi:10.1103/physrevb.107.155133 · Cited by 13
Quantum Mpemba Effect in Long-Range Spin Systems
Yamashika, S., & Ares, F. (2026) · Physical Review Letters · doi:10.1103/52y5-8kl2 · Cited by 13
Unified Definition of Exciton Coherence Length for Exciton–Phonon Coupled Molecular Aggregates
Jiang, T., Ren, J., & Shuai, Z. (2023) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.3c00812 · Cited by 13
Dynamics of correlation spreading in low-dimensional transverse-field Ising models
Kaneko, R., & Danshita, I. (2023) · Physical Review A · doi:10.1103/physreva.108.023301 · Cited by 14
Quantum Simulation of the Tricritical Ising Model in Tunable Josephson Junction Ladders
Maffi, L., Tausendpfund, N., Rizzi, M., & Burrello, M. (2024) · Physical Review Letters · doi:10.1103/physrevlett.132.226502 · Cited by 13
Quantum supercritical crossover with dynamical singularity
Wang, J., Lv, E., Li, X., Jin, Y., & Li, W. (2025) · Physical review. B./Physical review. B · doi:10.1103/hgwk-pzw2 · Cited by 14
Matrix product state fixed points of non-Hermitian transfer matrices
Tang, W., Verstraete, F., & Haegeman, J. (2025) · Physical review. B./Physical review. B · doi:10.1103/physrevb.111.035107 · Cited by 13
Self-citationKrumnow, C., Veis, L., Eisert, J., & Legeza, Ö. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.104.075137 · Cited by 14
Spin transport in disordered long-range interacting spin chain
Kloss, B., & Lev, Y. B. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.102.060201 · Cited by 14
Preparation for quantum simulation of the (1+1) -dimensional O(3) nonlinear σ model using cold atoms
Ciavarella, A. N., Caspar, S., Singh, H., & A, M. J. S. (2023) · Physical Review A · doi:10.1103/physreva.107.042404 · Cited by 19
Low-rank Riemannian eigensolver for high-dimensional Hamiltonians
Rakhuba, M., Novikov, A., & Oseledets, I. V. (2019) · Journal of Computational Physics · doi:10.1016/j.jcp.2019.07.003 · Cited by 13
Self-citationTheory of dissipation pathways in open quantum systems
Kim, C. W., & Franco, I. (2021) · The Journal of Chemical Physics · doi:10.1063/5.0038967 · Cited by 14
Cheng, J.-Q., Ning, Z., Wu, H.-Q., & Yao, D. (2024) · npj Quantum Materials · doi:10.1038/s41535-024-00705-8 · Cited by 12
Quantum quench dynamics of geometrically frustrated Ising models
Ali, A., Xu, H., Bernoudy, W., Nocera, A., King, A. D., & Banerjee, A. (2024) · Nature Communications · doi:10.1038/s41467-024-54701-4 · Cited by 12
Wu, A.-K., Kloss, B., Krinitsin, W., Fishman, M., Pixley, J. H., & Stoudenmire, E. M. (2025) · Physical review. B./Physical review. B · doi:10.1103/physrevb.111.035119 · Cited by 19
Hybrid Tree Tensor Networks for Quantum Simulation
Schuhmacher, J., Ballarin, M., Baiardi, A., Magnifico, G., Tacchino, F., Montangero, S., & Tavernelli, I. (2025) · PRX Quantum · doi:10.1103/prxquantum.6.010320 · Cited by 12
Disentangling critical quantum spin chains with Clifford circuits
Fan, C., Qian, X., Zhang, H.-C., Huang, R.-Z., Qin, M., & Xiang, T. (2025) · Physical review. B./Physical review. B · doi:10.1103/physrevb.111.085121 · Cited by 12
Variational approach to the dynamics of dissipative quantum impurity models
Qu, Y.-F., Stefanini, M., Shi, T., Esslinger, T., Gopalakrishnan, S., Marino, J., & Demler, E. (2025) · Physical review. B./Physical review. B · doi:10.1103/physrevb.111.155113 · Cited by 12
Theory of Fractional Quantum Hall Liquids Coupled to Quantum Light and Emergent Graviton-Polaritons
Bacciconi, Z., Xavier, H. B., Carusotto, I., Chanda, T., & Dalmonte, M. (2025) · Physical Review X · doi:10.1103/physrevx.15.021027 · Cited by 12
Improved Silbey-Harris polaron ansatz for the spin-boson model
He, S., Duan, L., & Chen, Q. (2018) · Physical review. B./Physical review. B · doi:10.1103/physrevb.97.115157 · Cited by 12
Weh, A., Zhang, Y., Östlin, A., Terletska, H., Bauernfeind, D., Tam, K.-M., Evertz, H. G., Byczuk, K., Vollhardt, D., & Chioncel, L. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.104.045127 · Cited by 12
RhoDyn: A ρ-TD-RASCI Framework to Study Ultrafast Electron Dynamics in Molecules
Kochetov, V., & Bokarev, S. I. (2021) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.1c01097 · Cited by 13
Slow dynamics of a mobile impurity interacting with an Anderson insulator
Sierant, P., Chanda, T., Lewenstein, M., & Zakrzewski, J. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.107.144201 · Cited by 12
Xu, Y., Cheng, Y., Song, Y., & Ma, H. (2023) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.2c01316 · Cited by 12
Muleady, S. R., Yang, M., White, S. R., & Rey, A. M. (2023) · Physical Review Letters · doi:10.1103/physrevlett.131.150401 · Cited by 13
Li, C., Yang, S., Xu, J., & Lin, H. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.107.085130 · Cited by 11
Dynamical correlation functions from complex time evolution
Cao, X., Lu, Y., Stoudenmire, E. M., & Parcollet, O. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.109.235110 · Cited by 11
Dorfner, M. F. X., Brey, D., Burghardt, I., & Ortmann, F. (2024) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.4c00751 · Cited by 11
Barata, J., & Mukherjee, S. (2025) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.111.l031901 · Cited by 11
Jeyaretnam, J., Bhore, T., Osborne, J. J., Halimeh, J. C., & Papić, Z. (2025) · Communications Physics · doi:10.1038/s42005-025-02039-8 · Cited by 25
Quantum reservoir probing of quantum phase transitions
Kobayashi, K., & Motome, Y. (2025) · Nature Communications · doi:10.1038/s41467-025-58751-0 · Cited by 11
LiV 2 O 4 : Hund-assisted orbital-selective Mottness
Grundner, M., Kugler, F. B., Parcollet, O., Schollwöck, U., Georges, A., & Hampel, A. (2025) · Physical review. B./Physical review. B · doi:10.1103/m42m-t4dm · Cited by 11
Second-order robust parallel integrators for dynamical low-rank approximation
Kusch, J. (2025) · BIT Numerical Mathematics · doi:10.1007/s10543-025-01073-w · Cited by 11
Partonic distribution functions and amplitudes using tensor network methods
Kang, Z.-B., Moran, N., Nguyen, P., & Qian, W. (2025) · Journal of High Energy Physics · doi:10.1007/jhep09(2025)176 · Cited by 11
Thermalization from quantum entanglement: Jet simulations in the massive Schwinger model
Florio, A., Frenklakh, D., Grieninger, S., Kharzeev, D. E., Palermo, A., & Shi, S. (2025) · Physical review. D/Physical review. D. · doi:10.1103/sgrx-jpp9 · Cited by 11
Hierarchical equations of motion solved with the multiconfigurational Ehrenfest ansatz
Shi, Z., Zhou, H., Huang, L., Xie, R., & Wang, L. (2025) · The Journal of Chemical Physics · doi:10.1063/5.0301142 · Cited by 13
Quench spectroscopy of a disordered quantum system
Villa, L., Thomson, S. J., & Sanchez-Palencia, L. (2021) · Physical Review A · doi:10.1103/physreva.104.l021301 · Cited by 11
Jiang, T., Ren, J., & Shuai, Z. (2021) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.1c02688 · Cited by 11
Projector formalism for kept and discarded spaces of matrix product states
Gleis, A., Li, J.-W., & von Delft, J. (2022) · Physical review. B./Physical review. B · doi:10.1103/physrevb.106.195138 · Cited by 11
Wójtowicz, G., Purkayastha, A., Zwolak, M., & Rams, M. M. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.107.035150 · Cited by 11
Ab-initio tree-tensor-network digital twin for quantum computer benchmarking in 2D
Jaschke, D., Pagano, A., Weber, S., & Montangero, S. (2024) · Quantum Science and Technology · doi:10.1088/2058-9565/ad5585 · Cited by 14
Ghahremani, B., & Babaee, H. (2024) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2024.117385 · Cited by 11
Efficient higher-order matrix product operators for time evolution
Damme, M. V., Haegeman, J., McCulloch, I. P., & Vanderstraeten, L. (2024) · SciPost Physics · doi:10.21468/scipostphys.17.5.135 · Cited by 11
Self-citationNanoscale engineering and dynamic stabilization of mesoscopic spin textures
Harkins, K. A., Fleckenstein, C., D’Souza, N., Schindler, P. M., Marchiori, D. A., Artiaco, C., Reynard-Feytis, Q., Basumallick, U., Beatrez, W., Pillai, A., et al. (2025) · Science Advances · doi:10.1126/sciadv.adn9021 · Cited by 11
Lambertson, E., Bashirova, D., Hunter, K. E., Hansen, B., & Zuehlsdorff, T. J. (2024) · The Journal of Chemical Physics · doi:10.1063/5.0224316 · Cited by 10
Quasi-Nambu-Goldstone modes in many-body scar models
Ren, J., Wang, Y., & Fang, C. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.110.245101 · Cited by 10
Chen, X. L., & Franco, I. (2025) · The Journal of Chemical Physics · doi:10.1063/5.0278591 · Cited by 10
Finding the phase diagram of strongly correlated disordered bosons using quantum quenches
Villa, L., Thomson, S. J., & Sanchez-Palencia, L. (2021) · Physical Review A · doi:10.1103/physreva.104.023323 · Cited by 10
Many-body localization in a tilted potential in two dimensions
Doggen, E. V. H., Gornyi, I. V., & Polyakov, D. G. (2022) · Physical review. B./Physical review. B · doi:10.1103/physrevb.105.134204 · Cited by 10
Hino, K., & Kurashige, Y. (2022) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.2c00243 · Cited by 10
Hierarchical Mapping for Efficient Simulation of Strong System-Environment Interactions
Xu, Y., Liu, C., & Ma, H. (2023) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.2c00851 · Cited by 10
Superexchange Liquefaction of Strongly Correlated Lattice Dipolar Bosons
Morera, I., Ołdziejewski, R., Astrakharchik, G. E., & Juliá-Díaz, B. (2023) · Physical Review Letters · doi:10.1103/physrevlett.130.023602 · Cited by 10
From Non-Markovian Dissipation to Spatiotemporal Control of Quantum Nanodevices
Lacroix, T., Lovett, B. W., & Chin, A. W. (2024) · Quantum · doi:10.22331/q-2024-04-03-1305 · Cited by 14
Growing extended Laughlin states in a quantum gas microscope: A patchwork construction
Palm, F. A., Kwan, J., Bakkali-Hassani, B., Greiner, M., Schollwöck, U., Goldman, N., & Grusdt, F. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.013198 · Cited by 10
Dynamical spectral response of fractonic quantum matter
Zechmann, P., Boesl, J., Feldmeier, J., & Knap, M. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.109.125137 · Cited by 10
Doggen, E. V. H., Gornyi, I. V., & Mirlin, A. D. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.109.224203 · Cited by 10
Environment induced dynamical quantum phase transitions in two-qubit Rabi model
Bello, G. D., Ponticelli, A., Pavan, F., Cataudella, V., Filippis, G. D., CANDIA, A. D., & Perroni, C. A. (2024) · Communications Physics · doi:10.1038/s42005-024-01855-8 · Cited by 15
Constrained dynamics and confinement in the two-dimensional quantum Ising model
Pavešič, L., Jaschke, D., & Montangero, S. (2025) · Physical review. B./Physical review. B · doi:10.1103/physrevb.111.l140305 · Cited by 10
Chiral polaron formation on the edge of topological quantum matter
Vashisht, A., Amelio, I., Vanderstraeten, L., Bruun, G. M., Diessel, O. K., & Goldman, N. (2025) · Nature Communications · doi:10.1038/s41467-025-60166-w · Cited by 10
Zeno and anti-Zeno effect in an open quantum system in the ultrastrong-coupling regime
He, S. M., Chen, Q., & Zheng, H. (2017) · Physical Review A · doi:10.1103/physreva.95.062109 · Cited by 10
Multiregion entanglement in locally scrambled quantum dynamics
Akhtar, A. A., & You, Y. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.102.134203 · Cited by 10
Sampling scheme for neuromorphic simulation of entangled quantum systems
Czischek, S., Pawlowski, J. M., Gasenzer, T., & Gärttner, M. (2019) · Physical review. B./Physical review. B · doi:10.1103/physrevb.100.195120 · Cited by 10
Fermionic Isometric Tensor Network States in Two Dimensions
Dai, Z., Wu, Y., Wang, T., & Zaletel, M. P. (2025) · Physical Review Letters · doi:10.1103/physrevlett.134.026502 · Cited by 9
Stochastic resonance in vibrational polariton chemistry
Ke, Y. (2025) · The Journal of Chemical Physics · doi:10.1063/5.0248419 · Cited by 9
Optimal symbolic construction of matrix product operators and tree tensor network operators
Çakır, H., Milbradt, R. M., & Mendl, C. B. (2025) · Physical review. B./Physical review. B · doi:10.1103/8993-8xn5 · Cited by 9
Zhang, S., Liu, Z., Bao, P., & Shi, Q. (2025) · The Journal of Chemical Physics · doi:10.1063/5.0266136 · Cited by 9
Augmenting a finite-temperature tensor network with Clifford circuits
Qian, X., Huang, J., & Qin, M. (2025) · Physical review. B./Physical review. B · doi:10.1103/gljy-1ykf · Cited by 9
Computing time-periodic steady-state currents via the time evolution of tensor network states
Strand, N. E., Vroylandt, H., & Gingrich, T. R. (2022) · The Journal of Chemical Physics · doi:10.1063/5.0099741 · Cited by 9
Phase transitions in the classical simulability of open quantum systems
Azad, F., Hallam, A., Morley, J. G., & Green, A. G. (2023) · Scientific Reports · doi:10.1038/s41598-023-35336-9 · Cited by 9
Thermal cycle and polaron formation in structured bosonic environments
Riva, A., Tamascelli, D., Dunnett, A., & Chin, A. W. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.108.195138 · Cited by 9
Metadata
- Authors
- Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B., & Verstraete, F.
- Affiliations
- Ghent University (BE)
- University of Tübingen (DE)
- Skolkovo Institute of Science and Technology (RU)
- Princeton University (US)
- University of Vienna (AT)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2016-10-10
- Volume
- 94
- Issue
- 16
- ISSN
- 2469-9950 (ISSN-L)
- 2469-9969
- OpenAlex
- W1580989833
- Cited by
- 804
- References
- 46
- Citations by year
- 2026: 88 · 2025: 148 · 2024: 106 · 2023: 73 · 2022: 79 · 2021: 91 · 2020: 89 · 2019: 56 · 2018: 38 · 2017: 28 · 2016: 7
- FWCI
- 20.33
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical review. B./Physical review. B (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Ghent University Academic Bibliography (Ghent University) (submittedVersion, other-oa)
- arXiv (Cornell University)
- Funders
- Russian Science Foundation (14-11-00659)
- Deutsche Forschungsgemeinschaft (SPP 1324, GRK 1838)
- Austrian Science Fund (FoQuS, ViCoM)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Mathematics › Numerical Analysis › Numerical Solvers for Ordinary Differential Equations
- Keywords
- matrix product states, time-dependent variational principle, Dirac-Frenkel variational principle, time evolution, optimization, density matrix renormalization group, time-evolving block decimation, long-range interactions, imaginary time evolution, tangent space projection
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
A language model drew the claims from the paper on 2026-10-05, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-05 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
