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

TL;DR

This paper introduces a numerical scheme for solving lattice Kohn-Sham equations with density-dependent exchange-correlation potentials at finite temperature, capturing derivative discontinuities and applied to fermionic atoms in traps.

Contribution

It proposes a self-consistent numerical method for lattice DFT with rapid density-dependent xc potentials using finite-temperature formalism.

Findings

Successfully applied to a 1D Hubbard model at finite temperature.

Observed density plateaus at low temperatures that melt at higher temperatures.

Demonstrated feasibility with a model of fermionic atoms in a harmonic trap.

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.