Particle-Number Projection and the Density Functional Theory

TL;DR

This paper explores the use of particle-number projection within Density Functional Theory for superconductors, addressing conceptual and numerical challenges due to the lack of explicit Hamiltonian or wave function.

Contribution

It highlights the conceptual and numerical difficulties in restoring particle number symmetry in DFT for superconductors, a topic with limited prior exploration.

Findings

Identifies key conceptual problems in particle-number projection

Discusses numerical difficulties in implementing the projection

Connects issues to the absence of explicit Hamiltonian or wave function

Abstract

In the framework of the Density Functional Theory for superconductors, we study the restoration of the particle number symmetry by means of the projection technique. Conceptual problems are outlined and numerical difficulties are discussed. Both are related to the fact that neither the many-body Hamiltonian nor the wave function of the system appear explicitly in the Density Functional Theory. Similar obstacles are encountered in self-consistent theories utilizing density-dependent effective interactions.