Isometric Tensor Network States in Two Dimensions

Zaletel, Michael P.; Pollmann, Frank

doi:10.1103/physrevlett.124.037201

Title: Isometric Tensor Network States in Two Dimensions

Journal Article · Wed Jan 01 00:00:00 EST 2020 · Physical Review Letters

DOI:https://doi.org/10.1103/physrevlett.124.037201· OSTI ID:1603571

Zaletel, Michael P. ^[1]; Pollmann, Frank ^[2]

Univ. of California, Berkeley, CA (United States)
Technische Univ. Munchen, Garching (Germany); Munich Center for Quantum Science and Technology (MCQST), Munchen (Germany)

Tensor-network states (TNS) are a promising but numerically challenging tool for simulating two-dimensional (2D) quantum many-body problems. We introduce an isometric restriction of the TNS ansatz that allows for highly efficient contraction of the network. Here we consider two concrete applications using this ansatz. First, we show that a matrix-product state representation of a 2D quantum state can be iteratively transformed into an isometric 2D TNS. Second, we introduce a 2D version of the time-evolving block decimation algorithm for approximating of the ground state of a Hamiltonian as an isometric TNS-which we demonstrate for the 2D transverse field Ising model.

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Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; German Research Foundation (DFG); European Union (EU); National Science Foundation (NSF)

Grant/Contract Number:: AC02-05CH11231; PO 1370/2-1; TRR80; 771537; PHY-1607611

OSTI ID:: 1603571

Journal Information:: Physical Review Letters, Vol. 124, Issue 3; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 29 works

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Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer Dborin, James; Wimalaweera, Vinul; Barratt, F. Nature Communications, Vol. 13, Issue 1 https://doi.org/10.1038/s41467-022-33737-4	journal	October 2022
Three-dimensional isometric tensor networks Tepaske, Maurits S. J.; Luitz, David J. Physical Review Research, Vol. 3, Issue 2 https://doi.org/10.1103/physrevresearch.3.023236	journal	June 2021
Holographic quantum algorithms for simulating correlated spin systems Foss-Feig, Michael; Hayes, David; Dreiling, Joan M. Physical Review Research, Vol. 3, Issue 3 https://doi.org/10.1103/physrevresearch.3.033002	journal	July 2021
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Isometric Tensor Network representation of string-net liquids Soejima, Tomohiro; Siva, Karthik; Bultinck, Nick arXiv https://doi.org/10.48550/arxiv.1908.07545	text	January 2019
On Stability of Tensor Networks and Canonical Forms Zhang, Yifan; Solomonik, Edgar arXiv https://doi.org/10.48550/arxiv.2001.01191	preprint	January 2020

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