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Cited by 261Quantum many-body systemsQuantum Computing Algorithms and ArchitectureQuantum Information and Cryptography

Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law

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Tagliacozzo, L., Evenbly, G., Vidal, G.·2009·Physical Review B
DOI 10.1103/physrevb.80.235127
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Abstract

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 one-dimensional systems, DMRG, MERA and TTN techniques scale favorably and can in principle treat very large systems.

    “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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Authors
Tagliacozzo, L., Evenbly, G., & Vidal, G.
Affiliations
The University of Queensland (AU)
ORCID
Venue
Physical Review B
Publisher
American Physical Society (APS)
Published
2009-12-18
Volume
80
Issue
23
ISSN
  • 1098-0121 (ISSN-L)
  • 1550-235X
DOI
10.1103/physrevb.80.235127
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
Licence
link.aps.org/licenses/aps-default-license (vor)
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 › Computer Science › Artificial Intelligence › 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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