Filter diagonalization of shell-model calculations

TL;DR

This paper introduces an extended filter diagonalization method based on the SS approach and COCG technique, enabling targeted eigenvalue calculations in shell-model physics, potentially replacing the Lanczos method.

Contribution

The authors extend the SS method with COCG to efficiently compute eigenvalues in specific energy ranges for shell-model calculations, addressing limitations of existing methods.

Findings

Successfully calculates eigenvalues in specified energy intervals.

Reduces inherent problems of the Lanczos method.

Demonstrates effectiveness in shell-model applications.

Abstract

We present a method of filter diagonalization for shell-model calculations. This method is based on the Sakurai and Sugiura (SS) method, but extended with help of the shifted complex orthogonal conjugate gradient (COCG) method. A salient feature of this method is that it can calculate eigenvalues and eigenstates in a given energy interval. We show that this method can be an alternative to the Lanczos method for calculating ground and excited states, as well as spectral strength functions. With an application to the $M$-scheme shell-model calculations we demonstrate that several inherent problems in the widely-used Lanczos method can be removed or reduced.