Monte Carlo shell model studies with massively parallel supercomputers

We present an overview of the advanced Monte Carlo shell model (MCSM), including its recent applications to no-core shell-model calculations and to large-scale shell-model calculations (LSSM) in the usual sense. For the ab initio no-core MCSM we show recent methodological developments, which include the evaluation of energy eigenvalues in an infinitely large model space by an extrapolation method. As an example of the application of the no-core MCSM, the cluster structure of Be isotopes is discussed. Regarding LSSM applications, the triple shape coexistence in ⁶⁸Ni and ⁷⁰Ni and the shape transition of Zr isotopes are clarified with the visualization of the intrinsic deformation of the MCSM wave function. General aspects of the code development of the MCSM on massively parallel computers are also briefly described. (invited comment)