Light Cone Matrix Product

TL;DR

This paper introduces a combined light-cone and matrix product approach to simulate long-time dynamics of quantum systems far from equilibrium, demonstrating extended simulation times and improved numerical stability.

Contribution

It presents a novel integration of light-cone and matrix product algorithms, including a modified iTEBD with enhanced stability and symmetry incorporation.

Findings

Simulated XXZ spin chain up to 22.5 units of time.

Observed potential revivals or shoulder in order parameter decay.

Extended simulation times due to combined methods.

Abstract

We show how to combine the light-cone and matrix product algorithms to simulate quantum systems far from equilibrium for long times. For the case of the XXZ spin chain at $\Delta=0.5$, we simulate to a time of $\approx 22.5$. While part of the long simulation time is due to the use of the light-cone method, we also describe a modification of the iTEBD algorithm with improved numerical stability, and we describe how to incorporate symmetry into this algorithm. While statistical sampling error means that we are not yet able to make a definite statement, the behavior of the simulation at long times indicates the appearance of either "revivals" in the order parameter as predicted previously or of a distinct shoulder in the decay of the order parameter.