Monte Carlo methods for many-body quantum systems

R. Guardiola

Malvin H. Kalos

G. Stoitcheva, W. E. Ormand, Daniel Neuhauser +1 more

We explore a novel and straightforward solution to the sign problem that has plagued the Auxiliary-field Monte Carlo (AFMC) method applied to many-body systems for more than a decade. We present a solution to the sign problem that has plagued the Auxiliary-field Monte Carlo (AFMC) method for more than a decade and report a breakthrough where excellent agreement between AFMC and exact CI calculations for fully realistic nuclear applications is achieved. This result offers the capability, unmatched by other methods, to achieve exact solutions for large-scale quantum many-body systems.

David M. Ceperley

Since its first description fifty years ago, the Metropolis Monte Carlo method has been used in a variety of different ways for the simulation of continuum quantum many‐body systems. This paper will consider some of the generalizations of the Metropolis algorithm employed in quantum Monte Carlo: Variational Monte Carlo, dynamical methods for projector monte carlo (i.e. diffusion Monte Carlo with rejection), multilevel sampling in path integral Monte Carlo, the sampling of permutations, cluster methods for lattice models, the penalty method for coupled electron‐ionic systems and the Bayesian analysis of imaginary time correlation functions.

Shiwei Zhang

Michio Honma, T. Mizusaki, Takaharu Otsuka

We propose a Monte Carlo method for solving the quantum many-body interacting systems. Mean fields dominating the structure of low-lying states are selected by a Monte Carlo method, which generates optimum many-body basis states for diagonalizing the Hamiltonian consisting of one- and two-body terms. Not only the ground state but also low-lying excited states are obtained with their wave functions. Results are examined by comparison to exact values.