Eur. Phys. J. B (2018) 91: 248
https://doi.org/10.1140/epjb/e2018-90186-5

Regular Article

Melting a Hubbard dimer: benchmarks of ‘ALDA’ for quantum thermodynamics^★

¹ Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Avenida dos Estados 5001, 09210-580 SantoAndré, São Paulo, Brazil
² Departamento de Física e Ciência Interdisciplinar, Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970 São Carlos, São Paulo,, Brazil
³ Department of Physics, University of York, York YO10 5DD, UK

^a e-mail: irene.damico@york.ac.uk

Received: 19 March 2018
Received in final form: 20 July 2018
Published online: 10 October 2018

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 the 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.