Variational ansatz for the superfluid Mott-insulator transition in optical lattices

TL;DR

This paper introduces a variational wave function approach to study the superfluid to Mott-insulator transition in one-dimensional bosonic lattice systems, effectively capturing local properties and phase crossover.

Contribution

It develops a variational method based on the quantum rotor model extended to the Bose-Hubbard model, providing an analytical tool for phase transition analysis.

Findings

Accurately describes local properties across interaction strengths

Captures the superfluid to Mott-insulator phase crossover

Agrees well with DMRG numerical results

Abstract

We develop a variational wave function for the ground state of a one-dimensional bosonic lattice gas. The variational theory is initally developed for the quantum rotor model and later on extended to the Bose-Hubbard model. This theory is compared with quasi-exact numerical results obtained by Density Matrix Renormalization Group (DMRG) studies and with results from other analytical approximations. Our approach accurately gives local properties for strong and weak interactions, and it also describes the crossover from the superfluid phase to the Mott-insulator phase.