A machine learning approach to excited states of quantum many-body systems*

We present a variational Monte Carlo method for determining dynamical properties and the spectral function of quantum many-body systems. Restricted Boltzmann machines (RBMs) are used to encode the Green's function of the system. First, the ground state wave function is calculated using a standard variational approach. The dynamical correlation function is then obtained by solving two linear systems of equations. We present a variational Monte Carlo approach to do so. This process has to be repeated for each value of frequency and momentum, but it can be easily parallelized. We illustrate it with applications to the Heisenberg model in one and two dimensions. Results show remarkable agreement with exact calculations on small systems and demonstrate that RBMs can also faithfully represent excited states.