Simulation of two dimensional quantum systems on an infinite lattice revisited: corner transfer matrix for tensor contraction

TL;DR

This paper enhances the iPEPS algorithm for infinite 2D quantum systems by integrating a corner transfer matrix approach, improving accuracy near critical points in models like the quantum Ising model.

Contribution

It introduces a modified iPEPS algorithm using CTMRG for environment computation, offering better estimates of physical quantities near criticality.

Findings

Improved estimation of order parameters near critical points.

Enhanced accuracy of correlators in the quantum Ising model.

Effective combination of CTMRG with imaginary time evolution.

Abstract

An extension of the projected entangled-pair states (PEPS) algorithm to infinite systems, known as the iPEPS algorithm, was recently proposed to compute the ground state of quantum systems on an infinite two-dimensional lattice. Here we investigate a modification of the iPEPS algorithm, where the environment is computed using the corner transfer matrix renormalization group (CTMRG) method, instead of using one-dimensional transfer matrix methods as in the original proposal. We describe a variant of the CTMRG that addresses different directions of the lattice independently, and use it combined with imaginary time evolution to compute the ground state of the two-dimensional quantum Ising model. Near criticality, the modified iPEPS algorithm is seen to provide a better estimation of the order parameter and correlators.