32 research outputs found
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
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
Numerical calculation of spectral functions of the Bose-Hubbard model using B-DMFT
We calculate the momentum dependent spectral function of the Bose-Hubbard
model on a simple cubic lattice in three dimensions within the bosonic
dynamical mean-field theory (B-DMFT). The continuous-time quantum Monte Carlo
method is used to solve the self-consistent B-DMFT equations together with the
maximum entropy method for the analytic continuation to real frequencies.
Results for weak, intermediate, and strong interactions are presented. In the
limit of weak and strong interactions very good agreement with results obtained
by perturbation theory is found. By contrast, at intermediate interactions the
results differ significantly, indicating that in this regime perturbative
methods fail do describe the dynamics of interacting bosons.Comment: Bigger figures in version 2; no significant changes in tex
Local moment approach to multi-orbital single impurity Anderson model; application to dynamical mean-field theory
Using a local moment approach of Logan et al. we developed a solver for a
multi-orbital single impurity Anderson model. The existence of the local
moments is taken from the outset and their values are determined through
variational principle by minimizing the corresponding ground state energy. The
method is used 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: 2 pages, 1 figur