Time-evolution methods for matrix-product states

TL;DR

This paper reviews and compares recent methods for simulating the time evolution of one-dimensional quantum many-body states using matrix-product states, highlighting their applications and differences.

Contribution

It provides a comprehensive comparison of various recent algorithms for time-evolving matrix-product states in finite quantum systems.

Findings

Different methods have unique advantages and limitations.

The methods are demonstrated on representative condensed matter problems.

The review clarifies the applicability of each approach.

Abstract

Matrix-product states have become the de facto standard for the representation of one-dimensional quantum many body states. During the last few years, numerous new methods have been introduced to evaluate the time evolution of a matrix-product state. Here, we will review and summarize the recent work on this topic as applied to finite quantum systems. We will explain and compare the different methods available to construct a time-evolved matrix-product state, namely the time-evolving block decimation, the MPO $W^\mathrm{II}$ method, the global Krylov method, the local Krylov method and the one- and two-site time-dependent variational principle. We will also apply these methods to four different representative examples of current problem settings in condensed matter physics.