# Thick-Restart Block Lanczos Method for Large-Scale Shell-Model Calculations

## TL;DR

This paper introduces a thick-restart block Lanczos method tailored for large-scale shell-model calculations, improving eigenvalue accuracy and computational efficiency, especially for highly excited states, and demonstrates its superior performance in a parallelized code.

## Contribution

The paper presents a novel thick-restart block Lanczos algorithm and its implementation in the KSHELL code, enhancing large-scale shell-model eigenvalue computations.

## Key findings

- Outperforms conventional Lanczos method in accuracy and efficiency.
- Enables detailed study of nuclear statistical properties.
- Effective for computing highly excited states with high eigenvalue density.

## Abstract

We propose a thick-restart block Lanczos method, which is an extension of the thick-restart Lanczos method with the block algorithm, as an eigensolver of the large-scale shell-model calculations. This method has two advantages over the conventional Lanczos method: the precise computations of the near-degenerate eigenvalues, and the efficient computations for obtaining a large number of eigenvalues. These features are quite advantageous to compute highly excited states where the eigenvalue density is rather high. A shell-model code, named KSHELL, equipped with this method was developed for massively parallel computations, and it enables us to reveal nuclear statistical properties which are intensively investigated by recent experimental facilities. We describe the algorithm and performance of the KSHELL code and demonstrate that the present method outperforms the conventional Lanczos method.