Dynamical mean-field theory for bosons

TL;DR

This paper introduces the bosonic dynamical mean-field theory (B-DMFT), a framework for analyzing bosonic lattice models by mapping them onto impurity problems, and demonstrates its application through phase diagrams and physical property calculations.

Contribution

The paper develops a comprehensive B-DMFT formalism with multiple derivation methods and applies it to compute phase diagrams and physical properties of bosonic lattice systems.

Findings

Finite temperature phase diagrams for bosonic Hubbard models

Condensate order parameter dependence on chemical potential

Critical exponents and kinetic energy behavior

Abstract

We discuss the recently developed bosonic dynamical mean-field (B-DMFT) framework, which maps a bosonic lattice model onto the selfconsistent solution of a bosonic impurity model with coupling to a reservoir of normal and condensed bosons. The effective impurity action is derived in several ways: (i) as an approximation to the kinetic energy functional of the lattice problem, (ii) using a cavity approach, and (iii) by using an effective medium approach based on adding a one-loop correction to the selfconsistently defined condensate. To solve the impurity problem, we use a continuous-time Monte Carlo algorithm based on a sampling of a perturbation expansion in the hybridization functions and the condensate wave function. As applications of the formalism we present finite temperature B-DMFT phase diagrams for the bosonic Hubbard model on a 3d cubic and 2d square lattice, the condensate order parameter as a function of chemical potential, critical exponents for the condensate, the approach to the weakly interacting Bose gas regime for weak repulsions, and the kinetic energy as a function of temperature.