Consistent Field Theory Across the Mott-Insulator to Superfluid Transition

TL;DR

This paper develops a consistent effective field theory for the Bose-Hubbard model that accurately describes the low-energy physics across the Mott insulator to superfluid transition, improving upon previous approximations.

Contribution

It introduces an EFT expanded around the correct mean-field vacuum, providing a more accurate description of the transition and low-energy excitations.

Findings

Reveals the structure of low-energy excitations at the transition

Identifies the emergence of massless and massive modes

Offers a unified framework for MI to SF transition analysis

Abstract

We employ a field-theoretical approach to analyze the Bose-Hubbard model on a lattice, with a focus on the low-energy properties across the Mott insulator (MI) to superfluid (SF) transition. Prior approaches approximated the partition function using cumulant expansions around the MI ground state, which, while accurate in the MI phase, lead to inaccuracies in the SF phase where the MI state is a false ground state. By expanding around the correct mean-field vacuum, we derive the effective field theory (EFT) governing the MI to SF transition. Through this, we reveal the underlying structure of the EFT governing the nucleation of low-energy excitations, particularly the massless and lowest massive modes, offering new insights into their emergence.