Non-Gaussian variational wave functions for interacting bosons on a lattice

A variational method for studying the ground state of strongly interacting quantum many-body bosonic systems is presented. Our approach constructs a class of extensive variational non-Gaussian wave functions which extend Gaussian states by means of nonlinear canonical transformations (NLCTs) on the fields of the theory under consideration. We illustrate this method with the one-dimensional Bose-Hubbard model for which the proposal presented here provides a family of approximate ground states at arbitrarily large values of the interaction strength. We find that, for different values of the interaction, the non-Gaussian NLCT-trial states sensibly improve the ground-state energy estimation when the system is in the Mott phase.