Dynamical Mean Field Theory for the Bose-Hubbard Model

TL;DR

This paper applies bosonic dynamical mean field theory to the Bose-Hubbard model, revealing phase diagrams and phase transitions, and providing insights relevant for experimental studies of strongly correlated bosonic systems.

Contribution

The paper extends bosonic DMFT to study the Bose-Hubbard model using exact diagonalization, producing phase diagrams and analyzing phase transitions at finite temperatures.

Findings

Identified Mott insulator, BEC, and normal phases.

Mapped phase diagrams on different parameter planes.

Analyzed finite-temperature phase crossover and transitions.

Abstract

The dynamical mean field theory (DMFT), which is successful in the study of strongly correlated fermions, was recently extended to boson systems [Phys. Rev. B {\textbf 77}, 235106 (2008)]. In this paper, we employ the bosonic DMFT to study the Bose-Hubbard model which describes on-site interacting bosons in a lattice. Using exact diagonalization as the impurity solver, we get the DMFT solutions for the Green's function, the occupation density, as well as the condensate fraction on a Bethe lattice. Various phases are identified: the Mott insulator, the Bose-Einstein condensed (BEC) phase, and the normal phase. At finite temperatures, we obtain the crossover between the Mott-like regime and the normal phase, as well as the BEC-to-normal phase transition. Phase diagrams on the $\mu/U-\tilde{t}/U$ plane and on the $T/U-\tilde{t}/U$ plane are produced ($\tilde{t}$ is the scaled hopping amplitude). We compare our results with the previous ones, and discuss the implication of these results to experiments.