Projection of angular momentum via linear algebra

TL;DR

This paper introduces a linear algebra-based method for projecting many-body quantum states with good angular momentum, offering a simpler alternative to traditional integral-based techniques.

Contribution

The authors present a novel linear algebra approach for angular momentum projection, reducing computational complexity and broadening applicability to other quantum numbers.

Findings

Method is competitive with standard quadrature techniques

Successfully applied to $^{48}$Cr and $^{60}$Fe in the $pf$ shell

Potential applicability to isospin and particle number projections

Abstract

Projection of many-body states with good angular momentum from an initial state is usually accomplished by a three-dimensional integral. We show how projection can instead be done by solving a straightforward system of linear equations. We demonstrate the method and give sample applications to $^{48}$Cr and $^{60}$Fe in the $pf$ shell. This new projection scheme, which is competitive against the standard numerical quadrature, should also be applicable to other quantum numbers such as isospin and particle number.