Symmetry restoration in Hartree-Fock-Bogoliubov based theories

TL;DR

This paper introduces a pfaffian formula for symmetry restoration in Hartree-Fock-Bogoliubov theories, enabling accurate projection of good quantum numbers and resolving sign ambiguity issues in wave function calculations.

Contribution

It provides a novel pfaffian-based method for symmetry projection in Bogoliubov wave functions, including excited states and linear combinations, addressing a longstanding computational challenge.

Findings

Successfully derives a pfaffian formula for symmetry projection.

Demonstrates application to particle number and angular momentum projection.

Resolves sign ambiguity problems in wave function symmetry restoration.

Abstract

We present a pfaffian formula for projection and symmetry restoration for wave functions of the general Bogoliubov form, including quasiparticle excited states and linear combinations of them. This solves a long-standing problem in calculating states of good symmetry, arising from the sign ambiguity of the commonly used determinant formula. A simple example is given of projecting good particle number and angular momentum from a Bogoliubov wave function in the Fock space of a single j-shell.