Two Dimensional Isometric Tensor Networks on an Infinite Strip

TL;DR

This paper extends isometric tensor network states (isoTNS) to infinite strip geometries, introduces algorithms for efficient state transformation and observable calculation, and applies these methods to simulate the 2D transverse field Ising model.

Contribution

It develops an infinite strip isoTNS framework with a new algorithm for tensor movement and demonstrates its application to 2D quantum systems.

Findings

Efficient evaluation of local observables in infinite strip isoTNS

Successful approximation of the 2D transverse field Ising model ground state

Introduction of an infinite version of the Moses Move algorithm

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 (iTEBD\textsuperscript{2}) and use it to approximate the ground state of the 2D transverse field Ising model on lattices of infinite strip geometry.