Time Averaged Density Matrix as an Optimization Problem

TL;DR

This paper introduces a novel method for computing time averaged density matrices in closed quantum systems by formulating it as a constraint overlap maximization problem, compatible with tensor network algorithms.

Contribution

The paper presents a new, simple approach to calculate time averaged density matrices that can be integrated with tensor network methods like MPOs.

Findings

Scaling behavior of time averaged expectation values

Variances of expectation values in non-integrable Ising chains

Operator space entanglement entropies analysis

Abstract

A new method is presented which allows time averaged density matrices of closed quantum systems to be computed via a constraint overlap maximization. Due to its simplicity, this method can be combined with algorithms based on tensor networks, as, e.g., matrix product operators (MPO). An algorithm is explained and several results for non-integrable Ising chains are given. Among them are scaling examples, time averaged expectation values, their variances and operator space entanglement entropies.