  We present a deep neural network (DNN)-based model (HubbardNet) to
variationally find the ground state and excited state wavefunctions of the
one-dimensional and two-dimensional Bose-Hubbard model. Using this model for a
square lattice with $M$ sites, we obtain the energy spectrum as an analytical
function of the on-site Coulomb repulsion, $U$, and the total number of
particles, $N$, from a single training. This approach bypasses the need to
solve a new hamiltonian for each different set of values $(U,N)$. Using
\texttt{HubbardNet}, we identify the two ground state phases of the
Bose-Hubbard model (Mott insulator and superfluid). We show that the
DNN-parametrized solutions are in excellent agreement with results from the
exact diagonalization of the hamiltonian, and it outperforms exact
diagonalization in terms of computational scaling. These advantages suggest
that our model is promising for efficient and accurate computation of exact
phase diagrams of many-body lattice hamiltonians.

Strongly Correlated Electrons