Quantum Monte Carlo diagonalization method for nuclear many body problem

Y. Alhassid

Mareki Honma, T. Mizusaki, Takaharu Otsuka

Francesco Pederiva, Alessandro Roggero, Kevin E. Schmidt

J. Bonnard, Olivier Juillet

The shell model provides a powerful framework for nuclear structure calculations. The nucleons beyond an inert magic core are confined in a valence shell and interact through an effective two-body potential generally determined from the G-matrix method. However, the applicability of the shell model remains limited by the exponential growth of the many-body space with the number of valence nucleons and with the size of the one-body space. The quantum Monte Carlo (QMC) methods may thus be considered as a potentially attractive alternative to the direct diagonalization of the Hamiltonian matrix. The many-body problem is indeed reduced to a set of stochastic one-body problems describing independent particles in a fluctuating external field. Up to date, the QMC approaches of the shell model lead to the ground-state and the thermodynamic properties, but a detailed spectroscopy of nuclei is not reachable. Furthermore, they suffer from a common pathology of fermionic QMC methods, namely the sign/phase problem, which strongly contaminates the convergence of the calculation. In this context, we will present a new QMC method, providing the "yrast spectroscopy" of nuclei, and in which the sign/phase problem is managed through the constrained path approximation that is widely used in the ab initio nuclear calculations and in condensed matter physics.

Takaharu Otsuka, Noritaka Shimizu, Seigo Haruyama +5 more

The Quantum Monte Carlo Diagonalization method for solving quantum many-body problems has been proposed, and its applications to the nuclear shell model have been extensively developed. This application is called Monte Carlo Shell Model. The actual numerical calculations of Monte Carlo Shell Model can be carried out very efficiently by a massive parallel computer, and indeed we have introduced one called Alphleet to RIKEN recently. A brief sketch of the Monte Carlo Shell Model and its parallel computing are presented.

Takaharu Otsuka, T. Mizusaki, Y. Utsuno +2 more

The formulation and recent applications of the Quantum Monte Carlo diagonalization (QMCD) method are reported. The QMCD has been proposed for solving the quantum many-body inteacting systems, providing us with energy eigenvalues, transition matrix elements and wave functions. Its application to the nuclear shell model is referred to as the Monte Carlo Shell Model. By the Monte Carlo Shell Model calculations, the level structure of low-lying states can be studied with realistic interactions, providing a useful tool for nuclear spectroscopy. The Monte Carlo Shell Model has been applied to the study of a variety of nuclei, and can be characterized as the importance truncation scheme to the full diagonalization which is infeasible in many cases due to extremely large dimensions.