Classical simulation of infinite-size quantum lattice systems in two spatial dimensions

TL;DR

This paper introduces an algorithm for simulating infinite two-dimensional quantum lattice systems, enabling ground state and time evolution computations for translationally invariant models, demonstrated on the quantum Ising model.

Contribution

It extends tensor network methods to infinite 2D systems, combining ideas from finite 2D PEPS and 1D iTEBD algorithms for the first time.

Findings

Successfully computed the ground state of the quantum Ising model.

Analyzed the second order quantum phase transition.

Demonstrated the algorithm's effectiveness in 2D quantum simulations.

Abstract

We present an algorithm to simulate two-dimensional quantum lattice systems in the thermodynamic limit. Our approach builds on the {\em projected entangled-pair state} algorithm for finite lattice systems [F. Verstraete and J.I. Cirac, cond-mat/0407066] and the infinite {\em time-evolving block decimation} algorithm for infinite one-dimensional lattice systems [G. Vidal, Phys. Rev. Lett. 98, 070201 (2007)]. The present algorithm allows for the computation of the ground state and the simulation of time evolution in infinite two-dimensional systems that are invariant under translations. We demonstrate its performance by obtaining the ground state of the quantum Ising model and analysing its second order quantum phase transition.