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K. Byczuk and D. Vollhardt We formulate a bosonic dynamical mean-field theory (B-DMFT) which provides a comprehensive, thermodynamically consistent framework for the theoretical investigation of correlated lattice bosons. The B-DMFT is applicable for arbitrary values of the coupling parameters and temperature and becomes exact in the limit of high spatial dimensions d or coordination number Z of the lattice. In contrast to its fermionic counterpart the construction of the B-DMFT requires different scalings of the hopping amplitudes with Z depending on whether the bosons are in their normal state or in the Bose-Einstein condensate. A detailed discussion of how this conceptual problem can be overcome by performing the scaling in the action rather than in the Hamiltonian itself is presented. The B-DMFT treats normal and condensed bosons on equal footing and thus includes the effects caused by their dynamic coupling. We employ the B-DMFT to solve a model of itinerant and localized, interacting bosons analytically. The local correlations are found to enhance the condensate density and the Bose-Einstein condensate (BEC) transition temperature T. This effect may be used experimentally to increase T of bosonic atoms in optical lattices. Phys. Rev. B 77, 235106 (2008) |
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