The DOI matches its Crossref record; 61 of the 61 references it cites were found in a registry or an index.
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
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- J. I. Latorre, 2004, Quantum Inf. Comput., 4, 48
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Orús, R. (2014) · Annals of Physics · doi:10.1016/j.aop.2014.06.013 · Cited by 2,255
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Laflorencie, N. (2016) · Physics Reports · doi:10.1016/j.physrep.2016.06.008 · Cited by 845
Efficient quantum state tomography
Cramer, M., Plenio, M. B., Flammia, S. T., Somma, R. D., Gross, D., Bartlett, S. D., Landon-Cardinal, O., Poulin, D., & Liu, Y.-K. (2010) · Nature Communications · doi:10.1038/ncomms1147 · Cited by 721
Tensor networks for complex quantum systems
Orús, R. (2019) · Nature Reviews Physics · doi:10.1038/s42254-019-0086-7 · Cited by 734
Simulating lattice gauge theories within quantum technologies
Bañuls, M. C., Blatt, R., Catani, J., Celi, A., Cirac, J. I., Dalmonte, M., Fallani, L., Jansen, K., Lewenstein, M., Montangero, S., et al. (2020) · The European Physical Journal D · doi:10.1140/epjd/e2020-100571-8 · Cited by 570
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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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