Melting a Hubbard dimer: benchmarks of `ALDA' for quantum thermodynamics

TL;DR

This paper investigates the effects of temperature on quantum work in a Hubbard dimer and evaluates the performance of density functional theory-inspired approximations, finding they work well at intermediate temperatures but struggle at high temperatures.

Contribution

It introduces a benchmark analysis of quantum thermodynamics in the Hubbard dimer and assesses the effectiveness of ALDA-based approximations across temperature regimes.

Findings

ALDA improves quantum work estimates at intermediate temperatures.

At high temperatures, ALDA-based methods fail to capture qualitative behavior.

Correlations significantly influence quantum work in the Hubbard dimer.

Abstract

The competition between evolution time, interaction strength, and temperature challenges our understanding of many-body quantum systems out-of-equilibrium. Here we consider a benchmark system, the Hubbard dimer, which allows us to explore all the relevant regimes and calculate exactly the related average quantum work. At difference with previous studies, we focus on the effect of increasing temperature, and show how this can turn competition between many-body interactions and driving field into synergy. We then turn to use recently proposed protocols inspired by density functional theory to explore if these effects could be reproduced by using simple approximations. We find that, up to and including intermediate temperatures, a method which borrows from ground-state adiabatic local density approximation improves dramatically the estimate for the average quantum work, including, in the adiabatic regime, when correlations are strong. However at high temperature and at least when based on the pseudo-LDA, this method fails to capture the counterintuitive qualitative dependence of the quantum work with interaction strength, albeit getting the quantitative estimates relatively close to the exact results.