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Cited by 225Quantum many-body systemsPhysics of Superconductivity and MagnetismQuantum Computing Algorithms and Architecture

Post-matrix product state methods: To tangent space and beyond

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Haegeman, Jutho, Osborne, Tobias J., Verstraete, Frank·2013·Physical Review B
DOI 10.1103/physrevb.88.075133
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Abstract

We develop in full detail the formalism of tangent states to the manifold of matrix product states, and show how they naturally appear in studying time evolution, excitations, and spectral functions. We focus on the case of systems with translation invariance in the thermodynamic limit, where momentum is a well-defined quantum number. We present some illustrative results and discuss analogous constructions for other variational classes. We also discuss generalizations and extensions beyond the tangent space, and give a general outlook towards post-matrix product methods.

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  • The mixed canonical form enables efficient truncation of an MPS.

    “The mixed canonical form enables us to truncate an MPS efficiently [12], which is one of the primitive tasks in any MPS toolbox.”

    From Tangent-space methods for uniform matrix product states (2019) · cites this paper as [12]

  • A right-to-left sweep composes the integrator with its adjoint, yielding a second-order symmetric method with error of order O(dt^3) for the state at t+2dt.

    “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 ).”

    From Unifying time evolution and optimization with matrix product states (2016) · cites this paper as [32]

  • One can transform the Hamiltonian expressed in terms of fermionic operators into a linear combination of tensor products of Pauli matrices that preserves the fermionic anticommutation relations.

    “While there are several methods for accomplishing this transform 180,181 , all result in a Hamiltonian that is a linear combination of tensor products of matrices { I, X, Y, Z } with I = ( 1 0 0 1 ) in such a way that preserves the fermionic anticommutation relations.”

    From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [181]

  • The Hamiltonian of molecular hydrogen in the minimal basis mapped to a four-qubit system using the Bravyi-Kitaev transformation takes a specific form.

    “The Hamiltonian of molecular hydrogen in the minimal basis mapped to a four-qubit system, using the Bravyi-Kitaev transformation, takes the following form 181,366 :”

    From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [181]

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Cited by

Sorted by citations

Authors
Haegeman, J., Osborne, T. J., & Verstraete, F.
Affiliations
  • Ghent University (BE)
  • Leibniz University Hannover (DE)
  • University of Vienna (AT)
ORCID
Venue
Physical Review B
Publisher
American Physical Society (APS)
Published
2013-08-20
Volume
88
Issue
7
ISSN
  • 1098-0121 (ISSN-L)
  • 1550-235X
DOI
10.1103/physrevb.88.075133
OpenAlex
W2084995257
Cited by
225
References
8
Citations by year
2026: 10 · 2025: 17 · 2024: 22 · 2023: 14 · 2022: 18 · 2021: 23 · 2020: 24 · 2019: 27 · 2018: 16 · 2017: 16 · 2016: 15 · 2015: 12 · 2014: 10 · 2013: 1
FWCI
6.52
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review B (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • Ghent University Academic Bibliography (Ghent University) (submittedVersion, other-oa)
  • Institutional Repository of Leibniz Universität Hannover (Leibniz Universität Hannover) (submittedVersion, cc-by-nc-nd)
  • arXiv (Cornell University)
  • Leibniz Universität Hannover
Funders
  • Austrian Science Fund
  • Fonds Wetenschappelijk Onderzoek
  • Vlaamse regering
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
  • Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Physics of Superconductivity and Magnetism
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
Keywords
matrix product states, tangent space, time evolution, excitation, spectral function, translation invariance, thermodynamic limit, momentum

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