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Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law
Open accessAbstract
This work explores the use of a tree tensor network ansatz to simulate the ground state of a local Hamiltonian on a two-dimensional lattice. By exploiting the entropic area law, the tree tensor network ansatz seems to produce quasiexact results in systems with sizes well beyond the reach of exact diagonalization techniques. We describe an algorithm to approximate the ground state of a local Hamiltonian on a $L\ifmmode\times\else\texttimes\fi{}L$ lattice with the topology of a torus. Accurate results are obtained for $L={4,6,8}$, whereas approximate results are obtained for larger lattices. As an application of the approach, we analyze the scaling of the ground-state entanglement entropy at the quantum critical point of the model. We confirm the presence of a positive additive constant to the area law for half a torus. We also find a logarithmic additive correction to the entropic area law for a square block. The single copy entanglement for half a torus reveals similar corrections to the area law with a further term proportional to $1/L$.
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“In the case of 1D systems, DMRG, MERA and TTN techniques scale favorably and can, in principle, treat very large systems [77-79].”
From Can one trust quantum simulators? (2012) · cites this paper as [79]
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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 renormalization group: Critical phenomena and the Kondo problem
Wilson, K. G. (1975) · Reviews of Modern Physics · doi:10.1103/revmodphys.47.773 · Cited by 4,582
The density-matrix renormalization group
Schollwöck, U. (2005) · Reviews of Modern Physics · doi:10.1103/revmodphys.77.259 · Cited by 3,323
Concentrating partial entanglement by local operations
Bennett, C. H., Bernstein, H. J., Popescu, S., & Schumacher, B. W. (1996) · Physical Review A · doi:10.1103/physreva.53.2046 · Cited by 3,151
Efficient Classical Simulation of Slightly Entangled Quantum Computations
Vidal, G. (2003) · Physical Review Letters · doi:10.1103/physrevlett.91.147902 · Cited by 2,368
Self-citationRigorous 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
Srednicki, M. (1993) · Physical Review Letters · doi:10.1103/physrevlett.71.666 · Cited by 1,858
Static Phenomena Near Critical Points: Theory and Experiment
Kadanoff, L. P., Götze, W., Hamblen, D. G., Hecht, R., Lewis, E. A. S., Palciauskas, V. V., RAYL, M., Swift, J. B., Aspnes, D. E., & Kane, J. W. (1967) · Reviews of Modern Physics · doi:10.1103/revmodphys.39.395 · Cited by 1,615
Scaling laws for ising models near Tc
Kadanoff, L. P. (1966) · Physics Physique Fizika · doi:10.1103/physicsphysiquefizika.2.263 · Cited by 1,615
Quantum source of entropy for black holes
Bombelli, L., Koul, R. K., Lee, J., & Sorkin, R. D. (1986) · Physical Review D · doi:10.1103/physrevd.34.373 · Cited by 1,439
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- J. I. Latorre, 2004, Quantum Inf. Comput., 4, 48
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Items 201–261 of 261
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High-Temperature Partition Functions and Classical Simulatability of Long-Range Quantum Systems
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Dubey, A., Zeybek, Z., & Schmelcher, P. (2025) · Physical review. B./Physical review. B · doi:10.1103/64hd-q4z5 · Cited by 6
Vovrosh, J., Julià-Farré, S., Krinitsin, W., Kaicher, M., Hayes, F. J., Gottlob, E., Kshetrimayum, A., Bidzhiev, K., Jäger, S. B., Schmitt, M., et al. (2026) · Physical Review Research · doi:10.1103/x4gs-g63p · Cited by 11
Universal entanglement of singular surfaces
Bueno, P., Myers, R. C., & Witczak‐Krempa, W. (2015) · Fortschritte der Physik · doi:10.1002/prop.201500072 · Cited by 1
Persistency of quantum non-multi-local correlations in noisy acyclic networks
Yang, S., Hou, J., & He, K. (2024) · Physica Scripta · doi:10.1088/1402-4896/ad35f7 · Cited by 1
Generalized Lanczos method for systematic optimization of neural-network quantum states
Wang, J.-Q., He, R.-Q., & Lu, Z.-Y. (2026) · Physical review. B./Physical review. B · doi:10.1103/m4c7-qz8l · Cited by 2
Optimal sampling of tensor networks targeting wave function's fast decaying tails
Ballarin, M., Silvi, P., Montangero, S., & Jaschke, D. (2025) · Quantum · doi:10.22331/q-2025-04-18-1714 · Cited by 4
Liu, G., Li, W., Deng, X.-Y., Su, G., & Tian, G.-S. (2013) · Solid State Communications · doi:10.1016/j.ssc.2013.10.023 · Cited by 1
Tensor Network Contraction and Multi-Linear Algebra
Ran, S.-J., Tirrito, E., Peng, C., Chen, X., Tagliacozzo, L., Su, G., & Lewenstein, M. (2020) · Lecture notes in physics · doi:10.1007/978-3-030-34489-4_5 · Cited by 1
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Ran, S.-J., Tirrito, E., Peng, C., Chen, X., Tagliacozzo, L., Su, G., & Lewenstein, M. (2020) · Lecture notes in physics · doi:10.1007/978-3-030-34489-4_4 · Cited by 1
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Howard, E. M., Chowdhury, I. S., & Nagle, I. (2021) · Lecture notes in networks and systems · doi:10.1007/978-3-030-77445-5_43 · Cited by 1
Ran, S.-J., Tirrito, E., Peng, C., Chen, X., Tagliacozzo, L., Su, G., & Lewenstein, M. (2020) · Lecture notes in physics · doi:10.1007/978-3-030-34489-4_1 · Cited by 1
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Moran, N. (2010) · Maynooth University ePrints and eTheses Archive (Maynooth University) · Cited by 1
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Jamshidi, S., & Morton, J. (2014) · Bulletin of the American Physical Society
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Ran, S.-J., Tirrito, E., Peng, C., Chen, X., Tagliacozzo, L., Su, G., & Lewenstein, M. (2020) · Lecture notes in physics · doi:10.1007/978-3-030-34489-4_2
Self-citationReyes, J. A. (2020) · Journal of International Crisis and Risk Communication Research
(2020) · SciPost Physics · doi:10.21468/scipost.report.1705
(2020) · SciPost Physics · doi:10.21468/scipost.report.2044
(2020) · SciPost Physics · doi:10.21468/scipost.report.1668
(2020) · SciPost Physics · doi:10.21468/scipost.report.1900
(2019) · SciPost Physics · doi:10.21468/scipost.report.1231
(2018) · SciPost Physics · doi:10.21468/scipost.report.612
(2019) · SciPost Physics Lecture Notes · doi:10.21468/scipost.report.830
(2018) · SciPost Physics · doi:10.21468/scipost.report.605
(2018) · SciPost Physics · doi:10.21468/scipost.report.648
(2019) · SciPost Physics · doi:10.21468/scipost.report.1245
(2018) · SciPost Physics · doi:10.21468/scipost.report.601
(2019) · SciPost Physics · doi:10.21468/scipost.report.1197
(2019) · SciPost Physics · doi:10.21468/scipost.report.822
Tindall, J., & Fishman, M. (2023) · SciPost Physics · doi:10.21468/scipost.report.7931
Tindall, J., & Fishman, M. (2023) · SciPost Physics · doi:10.21468/scipost.report.7878
(2024) · SciPost Physics Core · doi:10.21468/scipost.report.9069
Auxiliary-field Monte Carlo method for frustrated spin systems
Cai, N., 高, Y. 源. G., Li, W., & Qi, Y. (2025) · Chinese Physics B · doi:10.1088/1674-1056/ada758
Lacroix, T. (2025) · Springer theses · doi:10.1007/978-3-031-83143-0_3
Construction of Inequalities for Network Quantum Steering Detection
Jia, J., & He, K. (2025) · Axioms · doi:10.3390/axioms14080615
Bibliometric Analysis and Overview of Matrix Product States in the Bose-Hubbard Model
Gómez, J. S., & Rodríguez, K. (2025) · Ingeniería · doi:10.14483/23448393.22292
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Sharma, O., Manna, S., Rao, P. S., & Sreejith, G. J. (2026) · Physical review. B./Physical review. B · doi:10.1103/nvcg-mb1r
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Love, N., & Kovács, I. A. (2026) · New Journal of Physics · doi:10.1088/1367-2630/ae3795
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Upadhyay, S., Shayit, A., Zhang, T., Yuwono, S. H., DePrince, A. E., & Li, X. (2026) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.6c00098 · Cited by 1
Zhang, X., Xie, D., & Li, Y. (2026) · Entropy · doi:10.3390/e28050495
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Kaicher, M., Vovrosh, J., Dauphin, A., & Jäger, S. B. (2026) · Physical review. B./Physical review. B · doi:10.1103/drzd-7l5l
Larsson, H. R., Dé, B. L., & Gamboni, G. E. (2026) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.6c01138
Felser, T., & Montangero, S. (2026) · Graduate texts in physics · doi:10.1007/978-3-032-17635-6_7
Felser, T., & Montangero, S. (2026) · Graduate texts in physics · doi:10.1007/978-3-032-17635-6_5
Felser, T., & Montangero, S. (2026) · Graduate texts in physics · doi:10.1007/978-3-032-17635-6_1
Limits of Clifford disentangling in tensor network states
Masot-Llima, S., Sierant, P., Stornati, P., & García-Sáez, A. (2026) · Physical review. B./Physical review. B · doi:10.1103/5g5b-5rrz
Park, K. J., Peddireddy, D., & Aggarwal, V. (2026) · ACM Transactions on Quantum Computing · doi:10.1145/3821430
Hamiltonian Monte Carlo enhanced by exact diagonalization
Anonymous, Gisti, M., Luitz, D. J., Luu, T., & Ostmeyer, J. (2026) · Physical review. B./Physical review. B · doi:10.1103/z8tf-fwfn
Metadata
- Authors
- Tagliacozzo, L., Evenbly, G., & Vidal, G.
- Affiliations
- The University of Queensland (AU)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2009-12-18
- Volume
- 80
- Issue
- 23
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W2118564312
- Cited by
- 261
- References
- 61
- Citations by year
- 2026: 17 · 2025: 20 · 2024: 20 · 2023: 20 · 2022: 10 · 2021: 5 · 2020: 21 · 2019: 22 · 2018: 16 · 2017: 11 · 2016: 8 · 2015: 13 · 2014: 17 · 2013: 16 · 2012: 18
- FWCI
- 8.37
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review B (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- arXiv (Cornell University)
- 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 › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Keywords
- tree tensor networks, ground state simulation, local Hamiltonians, two-dimensional quantum systems, entanglement entropy, quantum critical point, logarithmic corrections
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