Year: 2023
Type: article
Abstract: The exact contraction of a generic two-dimensional (2D) tensor network state (TNS) is known to be exponentially hard, making simulation of 2D systems difficult. The recently introduced class of isometric TNS (isoTNS) represents a subset of TNS that allows for efficient simulation of such systems on finite square lattices. The isoTNS ansatz requires the identification of an ``orthogonality column'' of tensors, within which one-dimensional matrix product state (MPS) methods can be used for calculation of observables and optimization of tensors. Here we extend isoTNS to infinitely long strip geometries and introduce an infinite version of the Moses Move algorithm for moving the orthogonality column around the network. Using this algorithm, we iteratively transform an infinite MPS representation of a 2D quantum state into a strip isoTNS and investigate the entanglement properties of the resulting state. In addition, we demonstrate that the local observables can be evaluated efficiently. Finally, we introduce an infinite time-evolving block decimation algorithm (${\mathrm{iTEBD}}^{2}$) and use it to approximate the ground state of the 2D transverse field Ising model on lattices of infinite strip geometry.
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funders: U.S. Department of Energy, National Energy Research Scientific Computing Center, European Commission, Deutsche Forschungsgemeinschaft, Office of Science, European Research Council, RIKEN, Horizon 2020, Division of Mathematical Sciences, Basic Energy Sciences, Lawrence Berkeley National Laboratory
OpenAlex ID: W4380079593