Numerical evaluation and robustness of the quantum mean force Gibbs state

TL;DR

This paper presents a numerical method using an adapted TEMPO algorithm to accurately evaluate the Hamiltonian of Mean Force Gibbs states in strongly coupled quantum systems, confirming its effectiveness through comparisons and applications.

Contribution

The paper introduces an imaginary-time TEMPO method for computing the HMF Gibbs state in strongly coupled quantum systems, a novel approach in this context.

Findings

The HMF Gibbs state accurately predicts the steady state in a generalized spin-boson model.

Numerical dynamics align with the polaron master equation at strong coupling.

The method reveals reservoir-induced entanglement between qubits.

Abstract

We introduce a numerical method to determine the Hamiltonian of Mean Force (HMF) Gibbs state for a quantum system strongly coupled to a reservoir. The method adapts the Time Evolving Matrix Product Operator (TEMPO) algorithm to imaginary time propagation. By comparing the real-time and imaginary-time propagation for a generalized spin-boson model, we confirm that the HMF Gibbs state correctly predicts the steady state. We show that the numerical dynamics match the polaron master equation at strong coupling. We illustrate the potential of the imaginary-time TEMPO approach by exploring reservoir-induced entanglement between qubits.