Stochastic Estimation of Nuclear Level Density in the Nuclear Shell Model: An Application to Parity-Dependent Level Density in $^{58}$Ni

We introduce a novel method to obtain level densities in large-scale shell-model calculations. Our method is a stochastic estimation of eigenvalue count based on a shifted Krylov-subspace method, which enables us to obtain level densities of huge Hamiltonian matrices. This framework leads to a successful description of both low-lying spectroscopy and the experimentally observed equilibration of $J^\pi=2^+$ and $2^-$ states in $^{58}$Ni in a unified manner.