Abstract:

We present a deep neural network (DNN)-based model, the HubbardNet, to vari- ationally solve for the ground state and excited state wavefunctions of the one- dimensional and two-dimensional Bose-Hubbard model on a square lattice. Using this model, we obtain the Bose-Hubbard energy spectrum as an analytic function of the Coulomb parameter, U , and the total number of particles, N , from a single training, bypassing the need to solve a new hamiltonian for each different input. We show that the DNN-parametrized solutions have excellent agreement with exact di- agonalization while outperforming exact diagonalization in terms of computational scaling, suggesting that our model is promising for efficient, accurate computation of exact phase diagrams of many-body lattice hamiltonians.