Dresden 2006 – scientific programme
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TT: Tiefe Temperaturen
TT 25: Correlated Electrons - Poster Session
TT 25.48: Poster
Wednesday, March 29, 2006, 14:30–18:30, P1
Green functions for t-t′ hopping on the Bethe lattice — •M. Kollar1, M. Eckstein1, K. Byczuk1,2, N. Blümer3, P. van Dongen3, M. Radke de Cuba4, W. Metzner5, D. Tanasković6, V. Dobrosavljević6, G. Kotliar7, and D. Vollhardt1 — 1Theoretical Physics III, University of Augsburg — 2Institute of Theoretical Physics, Warsaw University, Poland — 3Institute of Physics, KOMET 337, University of Mainz — 4Aachen — 5MPI for Solid-State Research, Stuttgart — 6Dept. of Physics and NHMFL, Florida State University, USA — 7Dept. of Physics and Astronomy, Rutgers University, USA
We calculate the local Green function for a quantum-mechanical particle with hopping between nearest (t) and next-nearest neighbors (t′) on the Bethe lattice, where the on-site energies may alternate on sublattices [1]. For infinite connectivity the renormalized perturbation expansion is carried out by counting all non-self-intersecting paths, leading to an implicit equation for the local Green function. By integrating out branches of the Bethe lattice the same equation is obtained from a path integral approach for the partition function. This also provides the local Green function for finite connectivity. Finally, a recently developed topological approach [1] is extended to derive an operator identity which maps the problem onto the case of only nearest-neighbor hopping. We find that t′ hopping leads to an asymmetric spectrum with additional van-Hove singularities.
[1] M. Kollar et al., Ann. Phys. (Leipzig) 14, 642 (2005).
[2] M. Eckstein et al., Phys. Rev. B 71, 235119 (2005).