Comparison of Restricted Boltzmann Machines and Feedforward Neural Networks as Variational Ansätze for Quantum Many-Body Problems

Artificial neural networks have been shown to be powerful ansätze for quantum many-body problems. In this work, Gaussian-binary restricted Boltzmann machines and feedforward neural networks are used as trial wave functions for a variational Monte Carlo calculation. The ground state energy, wave function, and one-particle density are calculated for the Calogero-Sutherland model of bosons in one dimension. This continuous-space model is exactly solvable, allowing for a quantitative comparison between the two networks. These ansätze can be equivalently applied to any continuous-space system with a positive-definite ground state, but in return, they need far more parameters than a typical ansatz which has been tailored for a specific Hamiltonian. The reinforcement learning scheme used to train the networks will be discussed in detail, along with the computational costs.