Matrix Product States for dynamical simulation of infinite chains

TL;DR

This paper introduces a novel tensor network method using matrix product states for efficiently simulating the ground state and dynamics of infinite chains, enabling longer time evolution and handling non-invariant chains.

Contribution

The proposed method avoids finite size extrapolation and explicit bond truncation, allowing for more accurate and longer time simulations of infinite chains, including impurity models.

Findings

Enables longer time evolution in infinite chain simulations

Handles non-invariant infinite chains and impurity models

Eliminates the need for finite size extrapolation

Abstract

We propose a new method for computing the ground state properties and the time evolution of infinite chains based on a transverse contraction of the tensor network. The method does not require finite size extrapolation and avoids explicit truncation of the bond dimension along the evolution. By folding the network in the time direction prior to contraction, time dependent expectation values and dynamic correlation functions can be computed after much longer evolution time than with any previous method. Moreover, the algorithm we propose can be used for the study of some non-invariant infinite chains, including impurity models.