Accurate Variational Simulation of Lattice Bosons with Neural Quantum States*

In recent years, neural quantum states have emerged as a powerful variational method, consistently demonstrating remarkable accuracy in representing the ground-state wave function of a wide range of non-trivial Hamiltonians. In addition to spin problems, properly tailored networks have demonstrated their effectiveness in addressing problems involving other kinds of degrees of freedom, such as fermionic and continuous-variable systems. In spite of these successes, accurate neural representations of the ground state of lattice bosonic systems have remained elusive. We introduce a Jastrow Ansatz dressed with translationally equivariant many-body features generated by a deep neural network. We show that this variational state is able to faithfully represent the ground state of the 2D Bose-Hubbard Hamiltonian across all values of the interaction strength. This enables us to investigate the scaling of the entanglement entropy across the superfluid-to-Mott quantum phase transition and probe signatures of many-body processes involved in the depletion of the superfluid condensate that are not described by standard Bogoliubov theory.