5 research outputs found
The Mott-Hubbard Transition on the D=infinity Bethe Lattice
In view of a recent controversy we investigated the Mott-Hubbard transition
in D=infinity with a novel cluster approach. i) We show that any truncated
Bethe lattice of order n can be mapped exactly to a finite Hubbard-like
cluster. ii) We evaluate the self-energy numerically for n=0,1,2 and compare
with a series of self-consistent equation-of-motion solutions. iii) We find the
gap to open continously at the critical U_c~2.5t* (t = t* / sqrt{4d}). iv) A
low-energy theory for the Mott-Hubbard transition is developed and relations
between critical exponents are presented.Comment: Replaced with the published versio
Two-site dynamical mean-field theory
It is shown that a minimum realization of the dynamical mean-field theory
(DMFT) can be achieved by mapping a correlated lattice model onto an impurity
model in which the impurity is coupled to an uncorrelated bath that consists of
a single site only. The two-site impurity model can be solved exactly. The
mapping is approximate. The self-consistency conditions are constructed in a
way that the resulting ``two-site DMFT'' reduces to the previously discussed
linearized DMFT for the Mott transition. It is demonstrated that a reasonable
description of the mean-field physics is possible with a minimum computational
effort. This qualifies the simple two-site DMFT for a systematic study of more
complex lattice models which cannot be treated by the full DMFT in a feasible
way. To show the strengths and limitations of the new approach, the single-band
Hubbard model is investigated in detail. The predictions of the two-site DMFT
are compared with results of the full DMFT. Internal consistency checks are
performed which concern the Luttinger sum rule, other Fermi-liquid relations
and thermodynamic consistency.Comment: LaTeX, 14 pages, 8 eps figures included, Phys. Rev. B (in press