Scalability of DFT protocols for calculating quantum work in many-body systems

We report the application of DFT-inspired protocols to obtain thermodynamical quantities in many-body systems out of equilibrium. We discuss the scalability of the protocol recently proposed in Scientific Reports 7: 4655 (2017). Our study is focused on the extracted quantum work W in finite Hubbard lattices with L = 2, 4, 6, 8 sites driven by three different dynamics. We compare the exact W obtained by diagonalizing the full many body Hamiltonian with the estimate W_KS calculated using the Kohn-Sham auxiliary system. In the proposed DFT protocol, we use two approximations: (i) v_KS^BALDA, in which we consider the Kohn-Sham potentials as in the Bethe Ansatz Local Density Approximation for the homogeneous Hubbard and (ii) v_KS^exact, where we use an inversion scheme to obtain the exact exchange-correlation potential. Our results show that, in both approximations, the proposed protocol is able to accurately reproduce the quantum work in the low and intermediate coupling regimes. Additionally, while v_KS^exact performs better in all dynamical regimes (from sudden quench to adiabatic), BALDA captures better the qualitative profile of the quantum work of the interacting system.