Projection on particle number and angular momentum: Example of triaxial Bogoliubov quasiparticle states

TL;DR

This paper discusses the formalism and practical implementation of symmetry projection methods, specifically particle-number and angular-momentum projection of Bogoliubov quasiparticle states, to improve the description of self-bound many-body systems.

Contribution

It provides a comprehensive presentation of the projection formalism, explores efficient numerical techniques, and analyzes the effects of intrinsic symmetries in symmetry-breaking states.

Findings

Formalism of projection methods based on group theory.

Efficient algorithms for particle-number and angular-momentum projection.

Insights into the impact of intrinsic symmetries on projected states.

Abstract

Many quantal many-body methods that aim at the description of self-bound nuclear or mesoscopic electronic systems make use of auxiliary wave functions that break one or several of the symmetries of the Hamiltonian in order to include correlations associated with the geometrical arrangement of the system's constituents. Such reference states have been used already for a long time within self-consistent methods that are either based on effective valence-space Hamiltonians or energy density functionals, and they are presently also gaining popularity in the design of novel ab-initio methods. A fully quantal treatment of a self-bound many-body system, however, requires the restoration of the broken symmetries through the projection of the many-body wave functions of interest onto good quantum numbers. The goal of this work is three-fold. First, we want to give a general presentation of the formalism of the projection method starting from the underlying principles of group representation theory. Second, we want to investigate formal and practical aspects of the numerical implementation of particle-number and angular-momentum projection of Bogoliubov quasiparticle vacua, in particular with regard of obtaining accurate results at minimal computational cost. Third, we want to analyze the numerical, computational and physical consequences of intrinsic symmetries of the symmetry-breaking states when projecting them.