Theorems on ground-state phase transitions in Kohn-Sham models given by the Coulomb density functional

TL;DR

This paper presents theorems on the derivatives of the Coulomb density functional with respect to the coupling constant, revealing conditions under which phase transitions occur or accumulate, with implications for multi-reference density functional theory.

Contribution

It establishes rigorous theorems on phase transitions and level crossings in Kohn-Sham models with Coulomb density functionals, especially regarding their behavior as the coupling constant approaches one.

Findings

Phase transitions occur only at discrete points along the coupling constant axis.

Accumulation of phase transition points is prevented when the density is v-representable for all coupling constants.

The results have implications for multi-reference density functional theory.

Abstract

Some theorems on derivatives of the Coulomb density functional with respect to the coupling constant $\lambda$ are given. Consider an electron density $n_{GS}({\bf r})$ given by a ground state. A model Fermion system with the reduced coupling constant, $\lambda<1$, is defined to reproduce $n_{GS}({\bf r})$ and the ground state energy. Fixing the charge density, possible phase transitions as level crossings detected in a value of the reduced density functional happen only at discrete points along the $\lambda$ axis. If the density is $v$-representable also for $\lambda<1$, accumulation of phase transition points is forbidden when $\lambda\rightarrow 1$. Relevance of the theorems for the multi-reference density functional theory is discussed.