Recent Progress of Shell-Model Calculations, Monte Carlo Shell Model, and Quasi-Particle Vacua Shell Model

Nuclear shell model is a powerful approach to investigate nuclear structure microscopically. However, the computational cost of shell-model calculations becomes huge in medium-heavy nuclei. I briefly review the theoretical framework and the code developments of the conventional Lanczos diagonalization method for shell-model calculations. In order to go beyond the conventional diagonalization method, the Monte Carlo shell model and the quasiparticle-vacua shell model were introduced. I present some benchmark examples of these models