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Cited by 227Quantum many-body systemsQuantum Computing Algorithms and ArchitecturePhysics of Superconductivity and Magnetism

Infinite projected entangled pair states algorithm improved: Fast full update and gauge fixing

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Phien, Ho N., Bengua, Johann A., Tuan, Hoang D., Corboz, Philippe, Orús, Román·2015·Physical Review B
DOI 10.1103/physrevb.92.035142
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Abstract

The infinite projected entangled pair states (iPEPS) algorithm [J. Jordan et al., Phys. Rev. Lett. 101, 250602 (2008)] has become a useful tool in the calculation of ground-state properties of two-dimensional quantum lattice systems in the thermodynamic limit. Despite its many successful implementations, the method has some limitations in its present formulation which hinder its application to some highly entangled systems. The purpose of this paper is to unravel some of these issues, in turn enhancing the stability and efficiency of iPEPS methods. For this, we first introduce the fast full update scheme, where effective environment and iPEPS tensors are both simultaneously updated (or evolved) throughout time. As we shall show, this implies two crucial advantages: (i) dramatic computational savings and (ii) improved overall stability. In addition, we extend the application of the local gauge fixing, successfully implemented for finite-size PEPS [M. Lubasch et al., Phys. Rev. B 90, 064425 (2014)], to the iPEPS algorithm. We see that the gauge fixing not only further improves the stability of the method but also accelerates the convergence of the alternating least-squares sweeping in the (either ``full'' or ``fast full'') tensor update scheme. The improvement in terms of computational cost and stability of the resulting ``improved'' iPEPS algorithm is benchmarked by studying the ground-state properties of the quantum Heisenberg and transverse-field Ising models on an infinite square lattice.

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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 [71]

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Cited by

Sorted by citations

Authors
Phien, H. N., Bengua, J. A., Tuan, H. D., Corboz, P., & Orús, R.
Affiliations
  • University of Technology Sydney (AU)
  • Institute for Theoretical Physics Amsterdam (NL)
  • Johannes Gutenberg University Mainz (DE)
ORCID
Venue
Physical Review B
Publisher
American Physical Society (APS)
Published
2015-07-24
Volume
92
Issue
3
ISSN
  • 1098-0121 (ISSN-L)
  • 1550-235X
DOI
10.1103/physrevb.92.035142
OpenAlex
W210903271
Cited by
227
References
4
Citations by year
2026: 19 · 2025: 15 · 2024: 16 · 2023: 21 · 2022: 18 · 2021: 19 · 2020: 29 · 2019: 34 · 2018: 18 · 2017: 26 · 2016: 12
FWCI
9.49
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review B (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • UvA-DARE (University of Amsterdam) (submittedVersion, other-oa)
  • UTS ePRESS (University of Technology Sydney) (submittedVersion)
  • Data Archiving and Networked Services (DANS) (submittedVersion, other-oa)
  • arXiv (Cornell University)
Funders
  • Australian Research Council (DP130104617)
  • Johannes Gutenberg-Universität Mainz
  • Deutsche Forschungsgemeinschaft
  • Nederlandse Organisatie voor Wetenschappelijk Onderzoek
  • Ministerie van Onderwijs, Cultuur en Wetenschappen
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, alternating least squares, ground-state properties, quantum Heisenberg model, transverse-field Ising model, thermodynamic limit, computational efficiency, algorithm stability

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