Stochastic extension of the Lanczos method for nuclear shell-model calculations with variational Monte Carlo method

TL;DR

This paper introduces a novel variational Monte Carlo method based on Krylov subspaces for large-scale nuclear shell-model calculations, demonstrating systematic improvements over traditional approaches.

Contribution

It develops a new VMC framework utilizing Krylov subspaces and stochastic sampling, extending the Lanczos method for nuclear shell-model calculations.

Findings

Successfully applied to $^{48}$Cr and $^{60}$Zn

Provides systematically improved results

Relates to a small number of Lanczos iterations

Abstract

We propose a new variational Monte Carlo (VMC) approach based on the Krylov subspace for large-scale shell-model calculations. A random walker in the VMC is formulated with the $M$-scheme representation, and samples a small number of configurations from a whole Hilbert space stochastically. This VMC framework is demonstrated in the shell-model calculations of $^{48}$Cr and $^{60}$Zn, and we discuss its relation to a small number of Lanczos iterations. By utilizing the wave function obtained by the conventional particle-hole-excitation truncation as an initial state, this VMC approach provides us with a sequence of systematically improved results.