Berlin 2005 – scientific programme

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TT: Tiefe Temperaturen

TT 6: Correlated Electrons - (General) Theory I

TT 6.8: Talk

Friday, March 4, 2005, 15:45–16:00, TU H2053

Arbitrary-range hopping on the Bethe lattice: Exact results for densities of states and dynamical mean-field theory — •Marcus Kollar¹, Martin Eckstein¹, Krzysztof Byczuk², and Dieter Vollhardt¹ — ¹Theoretische Physik III, Elektronische Korrelationen und Magnetismus, Institut für Physik, Universität Augsburg, 86135 Augsburg — ²Institute of Theoretical Physics, Warsaw University, ul. Hoza 69, 00-681 Warszawa, Poland

We develop a new method which relates an arbitrary hopping Hamiltonian on the Bethe lattice to the Hamiltonian with nearest-neighbor hopping [1]. This provides an exact expression for the density of states for any hopping. We present analytic results for the DOS corresponding to hopping between nearest and next-nearest neighbors, and also for exponentially decreasing hopping amplitudes. Conversely it is possible to construct a hopping Hamiltonian on the Bethe lattice for any given DOS. We also derive the exact self-consistency equations arising in the context of dynamical mean-field theory, which lead to a new starting point for studies of the Hubbard-type models with frustration.

[1] M. Eckstein et al., cond-mat/0409730.