Lattice density functional theory at finite temperature with strongly density-dependent exchange-correlation potentials

Abstract

The derivative discontinuity of the exchange-correlation (xc) energy at integer particle number is a property of the exact, unknown xc functional of density functional theory (DFT) which is absent in many popular local and semilocal approximations. In lattice DFT, approximations exist which exhibit a discontinuity in the xc potential at half filling. However, due to convergence problems of the Kohn-Sham (KS) self-consistency cycle, the use of these functionals is mostly restricted to situations where the local density is away from half filling. Here a numerical scheme for the self-consistent solution of the lattice KS Hamiltonian with a local xc potential with rapid (or quasi-discontinuous) density dependence is suggested. The problem is formulated in terms of finite-temperature DFT where the discontinuity in the xc potential emerges naturally in the limit of zero temperature. A simple parametrization is suggested for the xc potential of the uniform 1D Hubbard model at finite temperature which is obtained from the solution of the thermodynamic Bethe ansatz. The feasibility of the numerical scheme is demonstrated by application to a model of fermionic atoms in a harmonic trap. The corresponding density profile exhibits a plateau of integer occupation at low temperatures which melts away for higher temperatures.

Interacting fermions in one-dimensional disordered lattices: Exploring localization and transport properties with lattice density-functional theories

“…[30][31][32][33][34][35][36][37][38][39] On the other hand, the use of lattice TDDFT to describe the nonequilibrium dynamics of Hubbard-like models is a rather new topic [40][41][42][43] ; firm conceptual ground was initially established for approaches based on lattice bond currents, [44][45][46] …”

“…Lattice (TD)DFT has also been used to investigate ultracold atoms loaded on optical lattices. 32,39,43,[59][60][61][62] These systems make it possible to study different ground-state and nonequilibrium scenarios for the Hubbard model 63 with high accuracy (because a precise tunability of the lattice parameters is possible) more 115117-2 directly and easily than in solid-state experiments. In 2D, the Hubbard model has been investigated via DFT on the graphene lattice.…”

Solving lattice density functionals close to the Mott regime

“…[37]) among which LDFT has become particularly useful. 21,38,39 Static and time-dependent [14][15][16] lattice DFT were indeed used to investigate the physics of Hubbard models with on-site interaction 13,[17][18][19][20][21][22] , Kondo models [23][24][25][26][27][28] , disordered interacting lattice models 31,32 and spin liquids 33 .…”

Strong Correlations in Density-Functional Theory: A Model of Spin-Charge and Spin–Orbital Separations

“…28 In terms of this variable, local-(spin)-density approximations for Hubbard chains and rings have been constructed, [29][30][31][32] including a recent extension to finite temperatures. 33 In this section, we chose the fully numerical Bethe-Ansatz local-density approximation (BALDA-FN) 31 …”