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Mott insulator to superfluid transition in the Bose-Hubbard model: a strong-coupling approach

K. Sengupta·N. Dupuis
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Abstract

We present a strong-coupling expansion of the Bose-Hubbard model which describes both the superfluid and the Mott phases of ultracold bosonic atoms in an optical lattice. By performing two successive Hubbard-Stratonovich transformations of the intersite hopping term, we derive an effective action which provides a suitable starting point to study the strong-coupling limit of the Bose-Hubbard model. This action can be analyzed by taking into account Gaussian fluctuations about the mean-field approximation as in the Bogoliubov theory of the weakly interacting Bose gas. In the Mott phase, we reproduce results of previous mean-field theories and also calculate the momentum distribution function. In the superfluid phase, we find a gapless spectrum and compare our results with the Bogoliubov theory.

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K. Sengupta, N. Dupuis. 2005-04-15. Mott insulator to superfluid transition in the Bose-Hubbard model: a strong-coupling approach. https://doi.org/10.1103/physreva.71.033629

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