Symmetry breaking in the self-consistent Kohn-Sham equations

Abstract

The Kohn-Sham (KS) equations determine, in a self-consistent way, the particle density of an interacting fermion system at thermal equilibrium. We consider a situation when the KS equations are known to have a unique solution at high temperatures and this solution is a uniform particle density. We show that, at zero temperature, there are stable solutions that are not uniform. We provide the general principles behind this phenomenon, namely the conditions when it can be observed and how to construct these non-uniform solutions. Two concrete examples are provided, including fermions on the sphere which are shown to crystallize in a structure that resembles the C${}_{60}$ molecule.

a few typos eliminated

References in corpus (4)

• Wigner Crystallization in mesoscopic 2D electron systems
• There are No Unfilled Shells in Hartree-Fock Theory
• Group theoretical analysis of symmetry breaking in two-dimensional quantum dots
• Density-functional theory of freezing of quantum liquids at zero temperature using exact liquid-state linear response

Cited by in corpus (6)

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• Computing the Self-Consistent Field in Kohn-Sham Density Functional Theory
• From the Hartree dynamics to the Vlasov equation
• Isospin-symmetry restoration within the nuclear density functional theory: formalism and applications
• Unique Solutions to Hartree-Fock Equations for Closed Shell Atoms
• Symmetry breaking in the periodic Thomas--Fermi--Dirac--von Weizs{ä}cker model