Exact solution of the Bose-Hubbard model on the Bethe lattice

Details Exact solution of the Bose-Hubbard model on the Bethe lattice Exact solution of the Bose-Hubbard model on the Bethe lattice

2009-04-20

arxiv.org/abs/0904.3075v2

Phys. Rev. B 80, 014524 (2009)

Physics

Condensed Matter

Quantum Gases

27 pages, 16 figures, minor corrections

Scientific paper

The exact solution of a quantum Bethe lattice model in the thermodynamic limit amounts to solve a functional self-consistent equation. In this paper we obtain this equation for the Bose-Hubbard model on the Bethe lattice, under two equivalent forms. The first one, based on a coherent state path integral, leads in the large connectivity limit to the mean field treatment of Fisher et al. [Phys. Rev. B {\bf 40}, 546 (1989)] at the leading order, and to the bosonic Dynamical Mean Field Theory as a first correction, as recently derived by Byczuk and Vollhardt [Phys. Rev. B {\bf 77}, 235106 (2008)]. We obtain an alternative form of the equation using the occupation number representation, which can be easily solved with an arbitrary numerical precision, for any finite connectivity. We thus compute the transition line between the superfluid and Mott insulator phases of the model, along with thermodynamic observables and the space and imaginary time dependence of correlation functions. The finite connectivity of the Bethe lattice induces a richer physical content with respect to its infinitely connected counterpart: a notion of distance between sites of the lattice is preserved, and the bosons are still weakly mobile in the Mott insulator phase. The Bethe lattice construction can be viewed as an approximation to the finite dimensional version of the model. We show indeed a quantitatively reasonable agreement between our predictions and the results of Quantum Monte Carlo simulations in two and three dimensions.

Affiliated with

Also associated with

No associations

Rating

Exact solution of the Bose-Hubbard model on the Bethe lattice does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Exact solution of the Bose-Hubbard model on the Bethe lattice, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Exact solution of the Bose-Hubbard model on the Bethe lattice will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-174424