Strong coupling expansion for the Bose-Hubbard and the Jaynes-Cummings lattice model

TL;DR

This paper develops a strong coupling expansion method using Kato-Bloch perturbation theory to analyze the Mott insulator to superfluid transition in Bose-Hubbard and Jaynes-Cummings lattice models, including disordered systems.

Contribution

It generalizes the strong coupling expansion to disordered systems and the Jaynes-Cummings model, providing a numerical diagram generation approach for these complex systems.

Findings

Results agree with VCA and DMRG for phase transition points.

Method successfully applied to disordered systems.

Comparison highlights advantages over existing techniques.

Abstract

A strong coupling expansion, based on the Kato-Bloch perturbation theory, which has recently been proposed by Eckardt et al. [Phys. Rev. B 79, 195131] and Teichmann et al. [Phys. Rev. B 79, 224515] is implemented in order to study various aspects of the Bose-Hubbard and the Jaynes-Cummings lattice model. The approach, which allows to generate numerically all diagrams up to a desired order in the interaction strength is generalized for disordered systems and for the Jaynes-Cummings lattice model. Results for the Bose-Hubbard and the Jaynes-Cummings lattice model will be presented and compared with results from VCA and DMRG. Our focus will be on the Mott insulator to superfluid transition.