Green’s Function Approach to the Bose-Hubbard Model

Matthias Ohliger, Axel Pelster

Fachbereich Physik und Forschungszentrum OPTIMAS, Technische Universit?t Kaiserslautern, Kaiserslautern, Germany; Hanse-Wissenschaftskolleg, Lehmkuhlenbusch 4, Delmenhorst, Germany.
Institut für Theoretische Physik, Freien Universit?t Berlin, Berlin, Germany.

DOI: 10.4236/wjcmp.2013.32020                

Abstract

We use a diagrammatic hopping expansion to calculate finite-temperature Green functions of the Bose-Hubbard model which describes bosons in an optical lattice. This technique allows for a summation of subsets of diagrams, so the divergence of the Green function leads to non-perturbative results for the boundary between the superfluid and the Mott phase for finite temperatures. Whereas the first-order calculation reproduces the seminal mean-field result, the second order goes beyond and shifts the phase boundary in the immediate vicinity of the critical parameters determined by high-precision Monte-Carlo simulations of the Bose-Hubbard model. In addition, our Green’s function approach allows for calculating the excitation spectrum both for zero and finite temperature and for determining the effective masses of particles and holes.

Keywords

Bose-Hubbard Model; Quantum Phase Transition; Phase Boundary

Conflicts of Interest

The authors declare no conflicts of interest.

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