Abstract:Key words Bethe lattice, frustration, dynamical mean-field theory, Green function.PACS 71.10.Fd, 71.27.+a
Dedicated to Bernhard Mühlschlegel on the occasion of his 80th birthdayWe calculate the local Green function for a quantum-mechanical particle with hopping between nearest and next-nearest neighbors on the Bethe lattice, where the on-site energies may alternate on sublattices. For infinite connectivity the renormalized perturbation expansion is carried out by counting all non-selfintersecting paths, leadin… Show more
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. It reproduces all previously investigated limits in parameter space such as the Beliaev-Popov and Hartree-Fock-Bogoliubov approximations and generalizes the existing mean-field theories of interacting bosons. The self-consistency equations of the B-DMFT are those of a bosonic single-impurity coupled to two reservoirs corresponding to bosons in the condensate and in the normal state, respectively. 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 TBEC. This effect may be used experimentally to increase TBEC of bosonic atoms in optical lattices.
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. It reproduces all previously investigated limits in parameter space such as the Beliaev-Popov and Hartree-Fock-Bogoliubov approximations and generalizes the existing mean-field theories of interacting bosons. The self-consistency equations of the B-DMFT are those of a bosonic single-impurity coupled to two reservoirs corresponding to bosons in the condensate and in the normal state, respectively. 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 TBEC. This effect may be used experimentally to increase TBEC of bosonic atoms in optical lattices.
“…The hopping amplitude between sites i and j is denoted by t ij , the local interaction potential is parametrized by U i , and the chemical potential is given by µ. In the following, we consider fermions on a bipartite lattice with a semi-elliptical model density of states (DOS), [36][37][38] which is characterized by the connectivity K. It is related to the lattice coordination number Z via K = Z − 1. The hopping amplitude t ij is assumed to be only non-zero between nearest neighbor sites i and j.…”
Section: Model Of Correlated Fermions In Speckle Disordered Opticmentioning
confidence: 99%
“…Within statistical DMFT, this PDF is determined by an ensemble with a large number N of Green's functions. On the Bethe lattice, the hybridization function is given as sum over diagonal cavity Green's functions G 26,37,38,47 , i.e.…”
Section: A Statistical Dynamical Mean-field Theorymentioning
Strongly correlated fermions in three-and two-dimensional optical lattices with experimentally realistic speckle disorder are investigated. We extend and apply the statistical dynamical mean-field theory, which treats local correlations non-perturbatively, to incorporate on-site and hopping-type randomness on equal footing. Localization due to disorder is detected via the probability distribution function of the local density of states. We obtain a complete paramagnetic ground state phase diagram for experimentally realistic parameters and find a strong suppression of the correlationinduced metal insulator transition due to disorder. Our results indicate that the Anderson-Mott and the Mott insulator are not continuously connected due to the specific character of speckle disorder. Furthermore, we discuss the effect of finite temperature on the single-particle spectral function.
“…which corresponds to nearest-neighbor hopping on the Bethe lattice [75,76,77,78], or a particular kind of long-range hopping on the hypercubic lattice [79]. In the following we prove that a similar relation holds for the nonequilibrium case: For the density of states (3.18) the self-energy can be eliminated from Eqs.…”
Section: Nonequilibrium Dmft: the Self-consistency Conditionmentioning
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