Numerical calculation of spectral functions of the Bose-Hubbard model using B-DMFT

TL;DR

This paper computes the momentum-dependent spectral functions of the three-dimensional Bose-Hubbard model using bosonic dynamical mean-field theory, revealing the limitations of perturbative methods at intermediate interactions.

Contribution

It introduces a numerical approach combining B-DMFT with quantum Monte Carlo and maximum entropy methods to analyze spectral functions across interaction regimes.

Findings

Excellent agreement with perturbation theory at weak and strong interactions

Significant deviations from perturbation theory at intermediate interactions

Demonstrates the failure of perturbative methods in certain regimes

Abstract

We calculate the momentum dependent spectral function of the Bose-Hubbard model on a simple cubic lattice in three dimensions within the bosonic dynamical mean-field theory (B-DMFT). The continuous-time quantum Monte Carlo method is used to solve the self-consistent B-DMFT equations together with the maximum entropy method for the analytic continuation to real frequencies. Results for weak, intermediate, and strong interactions are presented. In the limit of weak and strong interactions very good agreement with results obtained by perturbation theory is found. By contrast, at intermediate interactions the results differ significantly, indicating that in this regime perturbative methods fail do describe the dynamics of interacting bosons.