Dynamical mean field solution of the Bose-Hubbard model

TL;DR

This paper introduces a bosonic dynamical mean field theory (B-DMFT) approach for the Bose-Hubbard model, providing accurate phase diagrams and correlation functions using a novel Monte Carlo solution method.

Contribution

It develops the B-DMFT framework for the bosonic Hubbard model and introduces a continuous-time Monte Carlo solver for the impurity problem.

Findings

Accurate phase diagrams and correlation functions for the Bose-Hubbard model.

The Monte Carlo method is adaptable to various bosonic systems.

B-DMFT offers a practical approach for studying complex bosonic mixtures.

Abstract

We present the effective action and self-consistency equations for the bosonic dynamical mean field (B-DMFT) approximation to the bosonic Hubbard model and show that it provides remarkably accurate phase diagrams and correlation functions. To solve the bosonic dynamical mean field equations we use a continuous-time Monte Carlo method for bosonic impurity models based on a diagrammatic expansion in the hybridization and condensate coupling. This method is readily generalized to bosonic mixtures, spinful bosons, and Bose-Fermi mixtures.