Non-Gaussian Variational Wavefunctions for Interacting Bosons on the Lattice

TL;DR

This paper introduces a variational approach using non-Gaussian wavefunctions with nonlinear canonical transformations to better approximate the ground state of strongly interacting bosonic systems, demonstrated on the 1D Bose-Hubbard model.

Contribution

It develops a new class of non-Gaussian variational wavefunctions that extend Gaussian states via nonlinear canonical transformations for lattice boson systems.

Findings

Improves ground state energy estimates in the Mott phase.

Applicable to arbitrarily large interaction strengths.

Provides a family of approximate ground states for the Bose-Hubbard model.

Abstract

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 wavefunctions which extend Gaussian states by means of nonlinear canonical transformations (NLCT) 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.