Strong-coupling solution of the bosonic dynamical mean-field theory

TL;DR

This paper presents an analytical strong-coupling solution for bosonic dynamical mean-field theory, accurately capturing phase transitions and spectral properties of correlated bosons in the Hubbard model.

Contribution

It introduces a linked-cluster expansion approach to solve B-DMFT analytically in the strong-coupling regime, aligning well with numerical methods.

Findings

The analytical solution matches numerical results for phase diagrams.

Enhanced zero-momentum distribution near superfluid transition.

Spectral function evolution differs between interaction and density-driven transitions.

Abstract

We derive an approximate analytical solution of the self-consistency equations of the bosonic dynamical mean-field theory (B-DMFT) in the strong-coupling limit. The approach is based on a linked-cluster expansion in the hybridization function of normal bosons around the atomic limit. The solution is used to compute the phase diagram of the bosonic Hubbard model for different lattices. We compare our results with numerical solutions of the B-DMFT equations and numerically exact methods, respectively. The very good agreement with those numerical results demonstrates that our approach captures the essential physics of correlated bosons both in the Mott insulator and in the superfluid phase. Close to the transition into the superfluid phase the momentum distribution function at zero momentum is found to be strongly enhanced already in the normal phase. The linked-cluster expansion also allows us to compute dynamical properties such as the spectral function of bosons. The evolution of the spectral function across the transition from the normal to the superfluid phase is seen to be characteristically different for the interaction driven and density driven transition, respectively.