Eur. Phys. J. B (2016) 89: 95
https://doi.org/10.1140/epjb/e2016-60820-5

Regular Article

Degenerate approach to the mean field Bose-Hubbard Hamiltonian

Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk 142190, Moscow Region, Russia

^a e-mail: ryzhov@hppi.troitsk.ru

Received: 14 October 2015
Received in final form: 15 December 2015
Published online: 11 April 2016

Abstract

A degenerate variant of mean field perturbation theory for the on-site Bose-Hubbard Hamiltonian is presented. We split the perturbation into two terms and perform exact diagonalization in the two-dimensional subspace corresponding to the degenerate states. The final relations for the second order ground state energy and first order wave function do not contain singularities at integer values of the chemical potentials. The resulting equation for the phase boundary between superfluid and Mott states coincides with the prediction from the conventional mean field perturbation approach.