Variational optimization with infinite projected entangled-pair states
Open accessAbstract
An infinite projected entangled-pair state (iPEPS) is a powerful variational tensor network ansatz for two-dimensional ground states in the thermodynamic limit, and can be seen as a natural generalization of a matrix-product state to two dimensions. One of the main challenges in iPEPS simulations is the optimization of the tensors, i.e., finding the optimal variational parameters, in order to have the best representation of the ground state of a given Hamiltonian. The author presents a variational optimization scheme, in which the energy is minimized in an iterative way by sweeping over all the tensors in the ansatz, in a similar spirit as done in the density-matrix renormalization group method. Benchmark results for challenging problems are presented that show that the variational scheme yields considerably more accurate results than the previously best imaginary-time evolution algorithm, with a similar computational cost and with a faster convergence towards the ground state.
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The uniform MPS framework allows parametrizing fermionic states on the chain directly using the formalism of super vector spaces.
“However, the uniform MPS framework allows to parametrize fermionic states on the chain directly using the formalism of super vector spaces [72].”
From Tangent-space methods for uniform matrix product states (2019) · cites this paper as [72]
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Cites
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- Authors
- Corboz, P.
- Affiliations
- Institute for Theoretical Physics Amsterdam (NL)
- Corresponding author
- Corboz, Philippe
- ORCID
- Corboz, Philippe
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2016-07-14
- Volume
- 94
- Issue
- 3
- ISSN
- 2469-9950 (ISSN-L)
- 2469-9969
- OpenAlex
- W2348656099
- Cited by
- 234
- References
- 7
- Citations by year
- 2026: 15 · 2025: 27 · 2024: 11 · 2023: 19 · 2022: 27 · 2021: 42 · 2020: 35 · 2019: 21 · 2018: 20 · 2017: 15 · 2016: 2
- FWCI
- 9.14
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical review. B./Physical review. B (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- UvA-DARE (University of Amsterdam) (submittedVersion, other-oa)
- Data Archiving and Networked Services (DANS) (submittedVersion, other-oa)
- arXiv (Cornell University)
- Funders
- Nederlandse Organisatie voor Wetenschappelijk Onderzoek
- Ministerie van Onderwijs, Cultuur en Wetenschap
- Government of Canada
- Industry Canada
- Ministry of Research and Innovation
- 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 › Physics of Superconductivity and Magnetism
- Keywords
- infinite projected entangled pair states, variational optimization, matrix product states, thermodynamic limit, tensor optimization, density matrix renormalization group
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