Matrix product decomposition and classical simulation of quantum dynamics in the presence of a symmetry

TL;DR

This paper introduces an SU(2) invariant matrix product state representation and extends TEBD algorithm to efficiently simulate quantum dynamics in symmetric systems, demonstrated on a critical spin chain.

Contribution

It develops a refined SU(2) invariant MPS representation and an extended TEBD algorithm for better simulation of symmetric quantum systems.

Findings

The SU(2) invariant MPS is more efficient for symmetric states.

The extended TEBD outperforms standard TEBD in simulations.

Demonstrated on a critical quantum spin chain.

Abstract

We propose a refined matrix product state representation for many-body quantum states that are invariant under SU(2) transformations, and indicate how to extend the time-evolving block decimation (TEBD) algorithm in order to simulate time evolution in an SU(2) invariant system. The resulting algorithm is tested in a critical quantum spin chain and shown to be significantly more efficient than the standard TEBD.