Interacting Bose gases with restricted Boltzmann Machine

Abstract

We implement two different methods for solving many-body quantum mechanical systems from scratch, a variational Monte Carlo (VMC) method and a restricted Boltzmann Machine (RBM). We explore a confined Bose-Einstein condensate within a harmonic oscillator potential trap. The VMC uses a single variational parameter in order to describe the wave function and estimate the expectation value for the ground state energy. The RBM uses several tuning parameters such as biases and weights associated with the network to describe the NQS. Both methods use Metropolis sampling technique and gradient descent has been applied as optimization scheme.