Melting a Hubbard dimer: benchmarks of ‘ALDA’ for quantum thermodynamics
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.
- 9.C.A. Ullrich, Time-Dependent Density-Functional Theory: Concepts and Applications, (OUP, Oxford, 2011) Google Scholar
- 13.J.C. Smith, F. Sagredo, K. Burke, in Warming Up Density Functional Theory, (Springer Singapore, Singapore, 2018) p. 249 Google Scholar
- 28.K. Micadei, J.P.S. Peterson, A.M. Souza, R.S. Sarthour, I.S. Oliveira, G.T. Landi, T.B. Batalhão, R.M. Serra, E.Lutz, Reversing the thermodynamic arrow of time using quantum correlations, https://doi.org/arXiv:1711.03323v1 (2017)
- 31.L. Fusco, S. Pigeon, T.J.G. Apollaro, A. Xuereb, L. Mazzola, M. Campisi, A. Ferraro, M. Paternostro, G. De Chiara, Phys. Rev. X 4, 031029 (2014) Google Scholar
- 39.K. Kikoin, M. Kiselev, Y. Avishai. Dynamical Symmetries for Nanostructures. (Springer-Verlag, Wien, 2012) Google Scholar
Open AccessThis is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://doi.org/creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.