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.

14 pages, 11 figures

References in corpus (16)

• Many-Body Physics with Ultracold Gases
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• The ALPS project release 1.3: open source software for strongly correlated systems
• Local quantum criticality in confined fermions on optical lattices
• Towards a description of the Kondo effect using time-dependent density functional theory
• Signature of Mott-insulator transition with ultra-cold fermions in a one-dimensional optical lattice
• Luther-Emery Phase and Atomic-Density Waves in a Trapped Fermion Gas
• Simple parametrization for the ground-state energy of the infinite Hubbard chain incorporating Mott physics, spin-dependent phenomena and spatial inhomogeneity
• Broadening of the Derivative Discontinuity in Density Functional Theory
• Collective excitations in one-dimensional ultracold Fermi gases: a comparative study
• Successes and failures of Bethe Ansatz Density Functional Theory
• Electric field response of strongly correlated one-dimensional metals: a Bethe-Ansatz density functional theory study
• Ground-state properties of the one-dimensional attractive Hubbard model with confinement: a comparative study
• Lattice density-functional theory on graphene
• Interacting Fermi Gases in Disordered One-Dimensional Lattices
• Phases of Bosons or Fermions in confined optical lattices

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