Quantum quenches in two spatial dimensions using chain array matrix product states

TL;DR

The paper introduces a novel tensor network method combining integrability and matrix product states to simulate real-time dynamics in two-dimensional quantum systems, successfully applied to 2D quantum Ising model quenches.

Contribution

It presents a new approach for simulating 2D quantum dynamics using chain array matrix product states, extending tensor network techniques to infinite cylinders.

Findings

Non-analyticities in return probability during phase-crossing quenches

Method effectively simulates 2D quantum quenches

Applicable to infinite cylindrical geometries

Abstract

We describe a method for simulating the real time evolution of extended quantum systems in two dimensions. The method combines the benefits of integrability and matrix product states in one dimension to avoid several issues that hinder other applications of tensor based methods in 2D. In particular it can be extended to infinitely long cylinders. As an example application we present results for quantum quenches in the 2D quantum (2+1 dimensional) Ising model. In quenches that cross a phase boundary we find that the return probability shows non-analyticities in time.