Real time evolution at finite temperatures with operator space matrix product states

TL;DR

The paper introduces a method to simulate real-time evolution at finite temperatures in 1D quantum systems using operator space matrix product states, enabling efficient calculations of expectation values across temperatures and times.

Contribution

It presents a novel approach that expresses density matrices and observables as matrix product states, allowing independent and efficient simulation of finite-temperature dynamics.

Findings

Efficient simulation of density matrices and operators at finite temperatures.

Application demonstrated on XXZ and Anderson models.

Polynomial growth of resources for integrable systems.

Abstract

We propose a method to simulate the real time evolution of one dimensional quantum many-body systems at finite temperature by expressing both the density matrices and the observables as matrix product states. This allows the calculation of expectation values and correlation functions as scalar products in operator space. The simulations of density matrices in inverse temperature and the local operators in the Heisenberg picture are independent and result in a grid of expectation values for all intermediate temperatures and times. Simulations can be performed using real arithmetics with only polynomial growth of computational resources in inverse temperature and time for integrable systems. The method is illustrated for the XXZ model and the single impurity Anderson model.