61 research outputs found
Strong-coupling solution of the bosonic dynamical mean-field theory
We derive an approximate analytical solution of the self-consistency
equations of the bosonic dynamical mean-field theory (B-DMFT) in the
strong-coupling limit. The approach is based on a linked-cluster expansion in
the hybridization function of normal bosons around the atomic limit. The
solution is used to compute the phase diagram of the bosonic Hubbard model for
different lattices. We compare our results with numerical solutions of the
B-DMFT equations and numerically exact methods, respectively. The very good
agreement with those numerical results demonstrates that our approach captures
the essential physics of correlated bosons both in the Mott insulator and in
the superfluid phase. Close to the transition into the superfluid phase the
momentum distribution function at zero momentum is found to be strongly
enhanced already in the normal phase. The linked-cluster expansion also allows
us to compute dynamical properties such as the spectral function of bosons. The
evolution of the spectral function across the transition from the normal to the
superfluid phase is seen to be characteristically different for the interaction
driven and density driven transition, respectively.Comment: 8 pages, 6 figure
Local moment approach to multi-orbital Anderson and Hubbard models
The variational local moment approach (V-LMA), being a modification of the
method due to Logan {\it et al}., is presented here. The existence of local
moments is taken from the outset and their values are determined through
variational principle by minimizing the corresponding ground state energy. Our
variational procedure allows us to treat both fermi- and non-fermi liquid
systems with many orbitals as well as insulators without any additional
assumptions. It is proved by an explicit construction of the corresponding Ward
functional that the V-LMA belongs to the class of conserving approximations. As
an illustration, the V-LMA is used to solve the multi-orbital single impurity
Anderson model. The method is also applied to solve the dynamical mean-field
equations for the multi-orbital Hubbard model. In particular, the Mott-Hubbard
metal--insulator transition is addressed within this approach.Comment: 11 page
Mixtures of correlated bosons and fermions: Dynamical mean-field theory for normal and condensed phases
We derive a dynamical mean-field theory for mixtures of interacting bosons
and fermions on a lattice (BF-DMFT). The BF-DMFT is a comprehensive,
thermodynamically consistent framework for the theoretical investigation of
Bose-Fermi mixtures and is applicable for arbitrary values of the coupling
parameters and temperatures. It becomes exact in the limit of high spatial
dimensions d or coordination number Z of the lattice. In particular, the
BF-DMFT treats normal and condensed bosons on equal footing and thus includes
the effects caused by their dynamic coupling. Using the BF-DMFT we investigate
two different interaction models of correlated lattice bosons and fermions, one
where all particles are spinless (model I) and one where fermions carry a spin
one-half (model II). In model I the local, repulsive interaction between bosons
and fermions can give rise to an attractive effective interaction between the
bosons. In model II it can also lead to an attraction between the fermions.Comment: 11 pages, removed style-files for Greek letter
NRG for the bosonic single-impurity Anderson model: Dynamics
The bosonic single-impurity Anderson model (B-SIAM) is studied to understand
the local dynamics of an atomic quantum dot (AQD) coupled to a Bose-Einstein
condensation (BEC) state, which can be implemented to probe the entanglement
and the decoherence of a macroscopic condensate. Our recent approach of the
numerical renormalization group (NRG) calculation for the B-SIAM revealed a
zero-temperature phase diagram, where a Mott phase with local depletion of
normal particles is separated from a BEC phase with enhanced density of the
condensate. As an extension of the previous work, we present the calculations
of the local dynamical quantities of the B-SIAM which reinforce our
understanding of the physics in the Mott and the BEC phases.Comment: 12 pages, 13 figure
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