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

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.

Mott insulator–superfluid phase transition in two-band Bose–Hubbard models with gapless nodal lines

“…When  t U the interaction energy dominates the kinetic energy and the bosons tend to localization to form the MI. In order to address the properties of the MI, we use the strongcoupling expansion method [43,44]. In the imaginary-time functional integral formalism, the partition function of the system…”

“…n and n 0 is the occupation number of the ground state in the local limit that minimizes the eigenvalue  n . See [43,44] for detailed calculations of the action and local Green function G 1c .…”