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Exact solution of the Bose-Hubbard model on the Bethe lattice | | Guilhem Semerjian
; Marco Tarzia
; Francesco Zamponi
; | | Date: |
20 Apr 2009 | | Abstract: | The exact solution of a quantum Bethe lattice model in the thermodynamic
limit amounts to resolve 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 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 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 mean-field 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. | | Source: | arXiv, 0904.3075 | | Services: | Forum | Review | PDF | Favorites | |
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