Two Dimensional Isometric Tensor Networks on an Infinite Strip
arXiv:2211.14337 · doi:10.1103/PhysRevB.107.245118
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.
21 pages, 12 figures; Version accepted for publication
References in corpus (9)
- The density-matrix renormalization group in the age of matrix product states
- Classical simulation of infinite-size quantum lattice systems in one spatial dimension
- Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
- Accurate determination of tensor network state of quantum lattice models in two dimensions
- The iTEBD algorithm beyond unitary evolution
- Algorithms for finite Projected Entangled Pair States
- Fermionic Implementation of Projected Entangled Pair States Algorithm
- Sequentially generated states for the study of two dimensional systems
- Infinite Matrix Product States vs Infinite Projected Entangled-Pair States on the Cylinder: a comparative study