Excitation Spectrum and Momentum Distribution of Bose-Hubbard Model with On-site Two- and Three-body Interaction

TL;DR

This paper derives an effective action for the Bose-Hubbard model with two- and three-body interactions, analyzing phase transitions, excitation spectra, and momentum distributions in optical lattices, highlighting the impact of three-body interactions.

Contribution

It introduces a strong-coupling effective action for the Bose-Hubbard model with three-body interactions, enabling detailed analysis of phase transitions and excitations.

Findings

Three-body interactions significantly affect the excitation spectrum.

The superfluid-Mott insulator transition is characterized with Gaussian fluctuations.

Momentum distribution varies notably with three-body interaction strength.

Abstract

An effective action for Bose-Hubbard model with two- and three-body on-site interaction in a square optical lattice is derived in the frame of a strong-coupling approach developed by Sengupta and Dupuis. From this effective action, superfluid-Mott insulator (MI) phase transition, excitation spectrum and momentum distribution for two phases are calculated by taking into account Gaussian fluctuation about the saddle-point approximation. In addition the effects of three-body interaction are also discussed.