Finitely correlated states on quantum spin chains
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The parameterized quantum circuit features a one-dimensional connectivity pattern, making it suitable for representation using a Matrix Product State (MPS).
“The parameterized quantum circuit in our study features a one-dimensional connectivity pattern, making it suitable for representation using a Matrix Product State (MPS) [56], [57], [58].”
From Towards secondary structure prediction of longer mRNA sequences using a quantum-centric optimization scheme (2025) · cites this paper as [56]
The underlying structure of the constructive approach to universal resources for MQC can be described mathematically using matrix-product states or projected-entangled-pairs.
“The underlying structure of this approach can be described mathematically using the language of matrix-product-states or projected-entangled-pairs 18,86,87 .”
From Measurement-based quantum computation (2009) · cites this paper as [86]
Cites
The Resonating Valence Bond State in La 2 CuO 4 and Superconductivity
Anderson, P. W. (1987) · Science · doi:10.1126/science.235.4793.1196 · Cited by 7,666 · see citing works
Angular Momentum in Quantum Mechanics
Edmonds, A. R., & Mendlowitz, H. (1958) · Physics Today · doi:10.1063/1.3062519 · Cited by 4,303 · see citing works
Two soluble models of an antiferromagnetic chain
Lieb, É. H., Schultz, T. D., & Mattis, D. C. (1961) · Annals of Physics · doi:10.1016/0003-4916(61)90115-4 · Cited by 4,292 · see citing works
Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model
Werner, R. F. (1989) · Physical Review A · doi:10.1103/physreva.40.4277 · Cited by 4,062 · see citing works
Self-citationAngular Momentum in Quantum Mechanics
Edmonds, A. R. (1957) · Princeton University Press eBooks · doi:10.1515/9781400884186 · Cited by 3,881 · see citing works
Zur Theorie der Metalle: I. Eigenwerte und Eigenfunktionen der linearen Atomkette
Bethe, H. (1931) · Zeitschrift f�r Physik · doi:10.1007/bf01341708 · Cited by 3,768 · see citing works
Theory of Operator Algebras II
Takesaki, M. (2003) · Encyclopaedia of mathematical sciences · doi:10.1007/978-3-662-10451-4 · Cited by 3,257 · see citing works
Operator Algebras and Quantum Statistical Mechanics
Bratteli, O., & Robinson, D. W. (1997) · Springer eBooks · doi:10.1007/978-3-662-03444-6 · Cited by 3,080 · see citing works
Haldane, F. D. M. (1983) · Physics Letters A · doi:10.1016/0375-9601(83)90631-x · Cited by 2,888 · see citing works
Rigorous results on valence-bond ground states in antiferromagnets
Affleck, I., Kennedy, T., Lieb, E. H., & Tasaki, H. (1987) · Physical Review Letters · doi:10.1103/physrevlett.59.799 · Cited by 2,223 · see citing works
On the theory of metals. 1. Eigenvalues and eigenfunctions for the linear atomic chain
Bethe, H. A. (1931) · Cited by 1,934 · see citing works
Group Theory and its Applications to Physical Problems
Hamermesh, M., & Mullin, A. A. (1962) · American Journal of Physics · doi:10.1119/1.1941790 · Cited by 1,735 · see citing works
Takesaki, M. (1979) · Springer eBooks · doi:10.1007/978-1-4612-6188-9 · Cited by 1,629 · see citing works
Group theory and its application to physical problems
Hamermesh, M. (1962) · Physics Today · doi:10.1063/1.3050758 · Cited by 1,511 · see citing works
Valence bond ground states in isotropic quantum antiferromagnets
Affleck, I. K., Kennedy, T., Lieb, É. H., & Tasaki, H. (1988) · Communications in Mathematical Physics · doi:10.1007/bf01218021 · Cited by 1,477 · see citing works
Arveson, W. (1969) · Acta Mathematica · doi:10.1007/bf02392388 · Cited by 1,174 · see citing works
Positive functions on 𝐶*-algebras
Stinespring, W. F. (1955) · Proceedings of the American Mathematical Society · doi:10.1090/s0002-9939-1955-0069403-4 · Cited by 1,085 · see citing works
Rigorous Results on Valence-Bond Ground States in Antiferromagnets
Affleck, I. K., Kennedy, T., Lieb, É. H., & Tasaki, H. (2004) · Springer eBooks · doi:10.1007/978-3-662-06390-3_18 · Cited by 989 · see citing works
Operator Algebras and Quantum Statistical Mechanics
Bratteli, O., & Robinson, D. W. (1979) · Springer eBooks · doi:10.1007/978-3-662-02313-6 · Cited by 929 · see citing works
Ordering Energy Levels of Interacting Spin Systems
Lieb, E., & Mattis, D. (1962) · Journal of Mathematical Physics · doi:10.1063/1.1724276 · Cited by 882 · see citing works
On Next-Nearest-Neighbor Interaction in Linear Chain. I
Majumdar, C. K., & Ghosh, D. K. (1969) · Journal of Mathematical Physics · doi:10.1063/1.1664978 · Cited by 877 · see citing works
Magid, A. R., & Jacobson, N. S. (1986) · American Mathematical Monthly · doi:10.2307/2322348 · Cited by 833 · see citing works
The picture of low-lying excitations in the isotropic Heisenberg chain of arbitrary spins
Takhtajan, L. A. (1982) · Physics Letters A · doi:10.1016/0375-9601(82)90764-2 · Cited by 550 · see citing works
Injectivity and operator spaces
Choi, M.-D., & Effros, E. G. (1977) · Journal of Functional Analysis · doi:10.1016/0022-1236(77)90052-0 · Cited by 513 · see citing works
Phase transitions in quantum spin systems with isotropic and nonisotropic interactions
Dyson, F. J., Lieb, É. H., & Barry Simon, A. (1978) · Journal of Statistical Physics · doi:10.1007/bf01106729 · Cited by 471 · see citing works
A proof of part of Haldane's conjecture on spin chains
Affleck, I. K., & Lieb, É. H. (1986) · Letters in Mathematical Physics · doi:10.1007/bf00400304 · Cited by 405 · see citing works
Observation ofS=1/2 degrees of freedom in anS=1 linear-chain Heisenberg antiferromagnet
Hagiwara, M., Katsumata, K., Affleck, I. K., et al. (1990) · Physical Review Letters · doi:10.1103/physrevlett.65.3181 · Cited by 400 · see citing works
Exact solution of the one-dimensional isotropic Heisenberg chain with arbitrary spins S
Babujian, H. (1982) · Physics Letters A · doi:10.1016/0375-9601(82)90403-0 · Cited by 383 · see citing works
Topics in the Theory of Lifting
Tulcea, A. I., & Tulcea, C. I. (1969) · Springer eBooks · doi:10.1007/978-3-642-88507-5 · Cited by 379 · see citing works
Extended Heisenberg models of antiferromagnetism: Analogies to the fractional quantum Hall effect
Arovas, D. P., & Auerbach, A. (1988) · Physical Review Letters · doi:10.1103/physrevlett.60.531 · Cited by 296 · see citing works
A schwarz inequality for positive linear maps on $C^{\ast}$-algebras
Choi, M.-D. (1974) · Illinois Journal of Mathematics · doi:10.1215/ijm/1256051007 · Cited by 295 · see citing works
Antiferromagnetic model with known ground state
Majumdar, C. K. (1970) · Journal of Physics C Solid State Physics · doi:10.1088/0022-3719/3/4/019 · Cited by 277 · see citing works
Gibbs states of a one dimensional quantum lattice
Araki, H. (1969) · Communications in Mathematical Physics · doi:10.1007/bf01645134 · Cited by 252 · see citing works
Symmetric states of infinite tensor products of C∗-algebras
Størmer, E. (1969) · Journal of Functional Analysis · doi:10.1016/0022-1236(69)90050-0 · Cited by 200 · see citing works
A Proof of Part of Haldane’s Conjecture on Spin Chains
Affleck, I. K., & Lieb, É. H. (1986) · Springer eBooks · doi:10.1007/978-3-662-06390-3_17 · Cited by 198 · see citing works
Accardi, L. (1981) · Physics Reports · doi:10.1016/0370-1573(81)90070-3 · Cited by 191 · see citing works
Locally normal symmetric states and an analogue of de Finetti's theorem
Hudson, R. L., & Moody, G. R. (1976) · Probability Theory and Related Fields · doi:10.1007/bf00534784 · Cited by 170 · see citing works
Existence of N�el order in some spin-1/2 Heisenberg antiferromagnets
Kennedy, T., Lieb, É. H., & Shastry, B. S. (1988) · Journal of Statistical Physics · doi:10.1007/bf01023854 · Cited by 167 · see citing works
Markov Random Fields and Gibbs Ensembles
Spitzer, F. (1971) · American Mathematical Monthly · doi:10.1080/00029890.1971.11992710 · Cited by 158 · see citing works
Energy gaps and elementary excitations for certain VBS-quantum antiferromagnets
Knabe, S. (1988) · Journal of Statistical Physics · doi:10.1007/bf01019721 · Cited by 136 · see citing works
Exact Antiferromagnetic Ground States of Quantum Spin Chains
Fannes, M., Nachtergaele, B., & Werner, R. F. (1989) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/10/7/005 · Cited by 136 · see citing works
Self-citationLarge- n Limit of SU ( n ) Quantum "Spin" Chains
Affleck, I. K. (1985) · Physical Review Letters · doi:10.1103/physrevlett.54.966 · Cited by 127 · see citing works
q-deformations of the O(3) symmetric spin-1 Heisenberg chain
Batchelor, M. T., Mezincescu, L., Nepomechie, R. I., et al. (1990) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/23/4/003 · Cited by 111 · see citing works
Foundations of Quantum Mechanics and Ordered Linear Spaces
Hartkämper, A., & Neumann, H. (1974) · Lecture notes in physics · doi:10.1007/3-540-06725-6 · Cited by 110 · see citing works
Exact ground states for a class of antiferromagnetic Heisenberg models with short-range interactions
Klein, D. (1982) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/15/2/032 · Cited by 100 · see citing works
Pietsch, A. (1970) · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · doi:10.1002/zamm.19700500715 · Cited by 99 · see citing works
The spectra of q-state vertex models and related antiferromagnetic quantum spin chains
Klümper, A. (1990) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/23/5/023 · Cited by 93 · see citing works
Ground states of VBS models on cayley trees
Fannes, M., Nachtergaele, B., & Werner, R. F. (1992) · Journal of Statistical Physics · doi:10.1007/bf01055710 · Cited by 75 · see citing works
Self-citationvan den Broek, P. M. (1980) · Physics Letters A · doi:10.1016/0375-9601(80)90662-3 · Cited by 75 · see citing works
A two-dimensional isotropic quantum antiferromagnet with unique disordered ground state
Kennedy, T., Lieb, É. H., & Tasaki, H. (1988) · Journal of Statistical Physics · doi:10.1007/bf01011563 · Cited by 72 · see citing works
Valence bond ground states in a frustrated two-dimensional spin-1/2 Heisenberg antiferromagnet
Chayes, J., Chayes, L., & Kivelson, S. A. (1989) · Communications in Mathematical Physics · doi:10.1007/bf01244017 · Cited by 58 · see citing works
Valence bond states on quantum spin chains as ground states with spectral gap
Fannes, M., Nachtergaele, B., & Werner, R. F. (1991) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/24/4/005 · Cited by 58 · see citing works
Self-citationSpin-s quantum chains and Temperley-Lieb algebras
Batchelor, M. T., & Barber, M. N. (1990) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/23/1/004 · Cited by 46 · see citing works
Some exact excited states in a linear antiferromagnetic spin system
Caspers, W. J., & Magnus, W. (1982) · Physics Letters A · doi:10.1016/0375-9601(82)90603-x · Cited by 42 · see citing works
The peripheral point spectrum of schwarz operators onC *-algebras
Groh, U. (1981) · Mathematische Zeitschrift · doi:10.1007/bf01214608 · Cited by 36 · see citing works
A study of the bilinear-biquadratic spin-1 antiferromagnetic chain using the valence-bond basis
Chang, K., Affleck, I. K., Hayden, G. W., et al. (1989) · Journal of Physics Condensed Matter · doi:10.1088/0953-8984/1/1/014 · Cited by 34 · see citing works
On solvable models in classical lattice systems
Fannes, M., & Verbeure, A. F. (1984) · Communications in Mathematical Physics · doi:10.1007/bf01217350 · Cited by 30 · see citing works
Self-citationUniqueness of the translationally invariant ground state in quantum spin systems
Matsui, T. (1990) · Communications in Mathematical Physics · doi:10.1007/bf02125695 · Cited by 30 · see citing works
Complete analysis of two spin correlations of valence bond solid chains for all integer spins
Freitag, W. D., & M�ller-Hartmann, E. (1991) · The European Physical Journal B · doi:10.1007/bf01313409 · Cited by 29 · see citing works
Aspects of non-commutative order
Effros, E. G. (1978) · Lecture notes in mathematics · doi:10.1007/bfb0067387 · Cited by 21 · see citing works
FUNCTIONS OF MARKOV PROCESSES AND ALGEBRAIC MEASURES
Fannes, M., Nachtergaele, B., & Slegers, L. (1992) · Reviews in Mathematical Physics · doi:10.1142/s0129055x92000030 · Cited by 20 · see citing works
Self-citationExact ground states for a class of linear antiferromagnetic spin systems
Caspers, W. J. (1982) · Physica A Statistical Mechanics and its Applications · doi:10.1016/0378-4371(82)90141-8 · Cited by 20 · see citing works
Remarks on a quantum state extension problem
Werner, R. F. (1990) · Letters in Mathematical Physics · doi:10.1007/bf00429951 · Cited by 19 · see citing works
Self-citationExact ground states for a class of linear quantum spin systems
Caspers, W. J., & Magnus, W. (1983) · Physica A Statistical Mechanics and its Applications · doi:10.1016/0378-4371(83)90160-7 · Cited by 15 · see citing works
Kernel representation of completely positive Hilbert-Schmidt operators on standard forms
Schmitt, L. M., & Wittstock, G. (1982) · Archiv der Mathematik · doi:10.1007/bf01304816 · Cited by 12 · see citing works
C*-Algebras and Applications to Physics
Araki, H., & Kadison, R. V. (1978) · Lecture notes in mathematics · doi:10.1007/bfb0067386 · Cited by 12 · see citing works
Working with Quantum Markov States and their classical analogues
Nachtergaele, B. (1990) · Lecture notes in mathematics · doi:10.1007/bfb0085520 · Cited by 7 · see citing works
Self-citationEntropy estimates for finitely correlated states
Fannes, M., Nachtergaele, B., & Werner, R. F. (1992) · French digital mathematics library (Numdam) · Cited by 6 · see citing works
Self-citationEXACT GROUND STATES OF ONE-DIMENSIONAL VALENCE-BOND-SOLID HAMILTONIANS
Iske, P. L., & Caspers, W. J. (1987) · Modern Physics Letters B · doi:10.1142/s0217984987000326 · Cited by 2 · see citing works
SCALING PROPERTIES OF VALENCE-BOND-SOLIDS WITH A LINEAR STRUCTURE
Iske, P. L., & Caspers, W. J. (1988) · Modern Physics Letters B · doi:10.1142/s021798498800117x · Cited by 2 · see citing works
Functions of Markov processes and algebraic measures
Fannes, M., Nachtergaele, B., & Slegers, L. (1992) · Reports on Mathematical Physics · Cited by 2 · see citing works
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Verstraete, F., Cirac, J. I., & Latorre, J. I. (2009) · Physical Review A · doi:10.1103/physreva.79.032316 · Cited by 158 · see citing works
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Gharibian, S., Huang, Y., Landau, Z., & Shin, S. W. (2015) · Foundations and Trends® in Theoretical Computer Science · doi:10.1561/0400000066 · Cited by 144 · see citing works
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King, A. D., Nocera, A., Rams, M. M., Dziarmaga, J., Wiersema, R., Bernoudy, W., Raymond, J., Kaushal, N., Heinsdorf, N., Harris, R., et al. (2025) · Science · doi:10.1126/science.ado6285 · Cited by 138 · see citing works
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Tagliacozzo, L., & Vidal, G. (2011) · Physical Review B · doi:10.1103/physrevb.83.115127 · Cited by 104 · see citing works
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Foss-Feig, M., Hayes, D., Dreiling, J. M., Figgatt, C., Gaebler, J. P., Moses, S. A., Pino, J. M., & Potter, A. C. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.033002 · Cited by 100 · see citing works
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Marti, K. H., Bauer, B., Reiher, M., Troyer, M., & Verstraete, F. (2010) · New Journal of Physics · doi:10.1088/1367-2630/12/10/103008 · Cited by 87 · see citing works
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Perales, Á., & Vidal, G. (2008) · Physical Review A · doi:10.1103/physreva.78.042337 · Cited by 49 · see citing works
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Ganahl, M., Beall, J., Hauru, M., Lewis, A. G. M., Wojno, T., Yoo, J. H., Zou, Y., & Vidal, G. (2023) · PRX Quantum · doi:10.1103/prxquantum.4.010317 · Cited by 37 · see citing works
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Kumar, V., Alevras, D., Metkar, M., Welling, E., Cade, C., Niesen, I., Friedhoff, T., Park, J.-E., Shivpuje, S., LaDue, M., et al. (2025) · arXiv · doi:10.48550/arxiv.2505.05782 · Cited by 3 · see citing works
“The parameterized quantum circuit in our study features a one-dimensional connectivity pattern, making it suitable for representation using a Matrix Product State (MPS) [56], [57], [58].”
- Authors
- Fannes, M., Nachtergaele, B., & Werner, R. F.
- Affiliations
- KU Leuven (BE)
- University of Chile (CL)
- Dublin Institute For Advanced Studies (IE)
- Venue
- Communications in Mathematical Physics
- Published
- 1992-03
- Volume
- 144
- Issue
- 3
- Pages
- 443-490
- ISSN
- 0010-3616 (ISSN-L)
- 1432-0916
- OpenAlex
- W2074426935
- Cited by
- 1,422
- References
- 71
- Citations by year
- 2026: 43 · 2025: 77 · 2024: 74 · 2023: 54 · 2022: 65 · 2021: 71 · 2020: 82 · 2019: 90 · 2018: 73 · 2017: 76 · 2016: 58 · 2015: 76 · 2014: 69 · 2013: 71 · 2012: 49
- FWCI
- 5.06
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Communications in Mathematical Physics (publishedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Mathematics › Mathematical Physics › Advanced Operator Algebra Research
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
- Keywords
- quantum spin chains, translation invariant states, valence bond states, ergodic decomposition, Néel state, exponential decay of correlations, ground state, spectral gap, finite-range interactions, one-dimensional antiferromagnet
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