Quantum heat statistics with time-evolving matrix product operators

TL;DR

This paper introduces a numerically exact method using time-evolving matrix product operators to analyze heat transfer statistics in non-Markovian open quantum systems, revealing the importance of system-reservoir correlations.

Contribution

It develops a novel computational approach for full counting statistics of heat transfer in non-Markovian quantum systems, applicable to complex models like the spin-boson.

Findings

System-reservoir correlations significantly affect heat statistics at low temperatures.

A variational theory accurately explains numerical results.

A fluctuation-dissipation relation links mean and variance at high temperature.

Abstract

We present a numerically exact method to compute the full counting statistics of heat transfer in non-Markovian open quantum systems, which is based on the time-evolving matrix product operator (TEMPO) algorithm. This approach is applied to the paradigmatic spin-boson model in order to calculate the mean and fluctuations of the heat transferred to the environment during thermal equilibration. We show that system-reservoir correlations make a significant contribution to the heat statistics at low temperature and present a variational theory that quantitatively explains our numerical results. We also demonstrate a fluctuation-dissipation relation connecting the mean and variance of the heat distribution at high temperature. Our results reveal that system-bath interactions make a significant contribution to heat transfer even when the dynamics of the open system is effectively Markovian. The method presented here provides a flexible and general tool to predict the fluctuations of heat transfer in open quantum systems in non-perturbative regimes.