Classical Simulation of Infinite-Size Quantum Lattice Systems in Two Spatial Dimensions
Open accessAbstract
We present an algorithm to simulate two-dimensional quantum lattice systems in the thermodynamic limit. Our approach builds on the projected entangled-pair state algorithm for finite lattice systems [F. Verstraete and J. I. Cirac, arxiv:cond-mat/0407066] and the infinite time-evolving block decimation algorithm for infinite one-dimensional lattice systems [G. Vidal, Phys. Rev. Lett. 98, 070201 (2007)10.1103/PhysRevLett.98.070201]. The present algorithm allows for the computation of the ground state and the simulation of time evolution in infinite two-dimensional systems that are invariant under translations. We demonstrate its performance by obtaining the ground state of the quantum Ising model and analyzing its second order quantum phase transition.
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The virtual degrees of freedom in an MPS transform under a projective representation of the symmetry group.
“This implies that the virtual degrees of freedom in the MPS transform under a projective representation of the symmetry group, a property that has led to the classification of symmetryprotected topological phases in one dimension using MPS [70,71].”
From Tangent-space methods for uniform matrix product states (2019) · cites this paper as [70]
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Self-citationLight-cone-like spreading of correlations in a quantum many-body system
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“This truncation can be done by a purely local singular-value decomposition – the so-called simple-update [80] algorithm – or by taking the full PEPS wavefunction into account – the full-update [81] or fast full-update algorithm [82].”
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- Authors
- Jordan, J., Orús, R., Vidal, G., Verstraete, F., & Cirac, J. I.
- Affiliations
- The University of Queensland (AU)
- University of Vienna (AT)
- Max Planck Institute of Quantum Optics (DE)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2008-12-18
- Volume
- 101
- Issue
- 25
- Pages
- 250602-250602
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2167325579
- Cited by
- 710
- References
- 4
- Citations by year
- 2026: 37 · 2025: 54 · 2024: 39 · 2023: 38 · 2022: 48 · 2021: 66 · 2020: 67 · 2019: 51 · 2018: 42 · 2017: 51 · 2016: 34 · 2015: 27 · 2014: 35 · 2013: 22 · 2012: 34
- FWCI
- 12.58
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Ghent University Academic Bibliography (Ghent University) (submittedVersion, other-oa)
- Max Planck Institute for Plasma Physics (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- 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 › Condensed Matter Physics › Theoretical and Computational Physics
- Keywords
- projected entangled pair states, infinite time-evolving block decimation, thermodynamic limit, translationally invariant systems, ground state calculation, time evolution simulation, quantum Ising model, second-order quantum phase transition
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