Density Functional Theory with Spatial-Symmetry Breaking and Configuration Mixing

TL;DR

This paper extends density functional theory by incorporating spatial symmetry breaking and configuration mixing, leading to coupled equations that exactly reformulate the many-body problem with explicit collective degrees of freedom.

Contribution

It introduces a generalized density functional approach with explicit collective coordinates, enabling exact reformulation of many-body problems through coupled local Schrödinger and Kohn-Sham equations.

Findings

Derivation of coupled equations for collective wave function and density

Exact reformulation of many-body problem with collective degrees of freedom

Framework for determining density- and collective-wave-function-dependent terms

Abstract

This article generalizes the notion of the local density of a many-body system to introduce collective coordinates as explicit degrees of freedom. It is shown that the energy of the system can be expressed as a functional of this object. The latter can in turn be factorized as the product of the square of a collective wave function and a normalized collective-coordinate-dependent density. Energy minimization translates into a set of coupled equations, i.e. a local Schr\"odinger equation for the collective wave function and a set of Kohn-Sham equations for optimizing the normalized density at each point in the collective space. These equations reformulate the many-body problem exactly provided one is able to determine density- and collective-wave-function-dependent terms of the collective mass and potential which play a similar role to the exchange-correlation term in electronic Kohn-Sham density functional theory.