Isometric Tensor Network States in Two Dimensions

Journal Article · 31 December 2019 · Physical Review Letters

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

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

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1. Univ. of California, Berkeley, CA (United States)
2. 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.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: European Union (EU); German Research Foundation (DFG); National Science Foundation (NSF); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division
• Grant/Contract Number: AC02-05CH11231
• OSTI ID: 1603571
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 3 Vol. 124; ISSN 0031-9007; ISSN PRLTAO
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English