Green functions for nearest- and next-nearest-neighbor hopping on the Bethe lattice

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dc.creatorKollar, M.
dc.creatorEckstein, M.
dc.creatorByczuk, K.
dc.creatorBlümer, N.
dc.creatorvan Dongen, P.
dc.creatorde Cuba, M. H. Radke
dc.creatorMetzner, W.
dc.creatorTanaskovic, D.
dc.creatorDobrosavljevic, V.
dc.creatorKotliar, G.
dc.creatorVollhardt, D.
dc.date2005-04-25
dc.date2005-08-29
dc.date.accessioned2026-07-07T03:04:55Z
dc.date.available2026-07-07T03:04:55Z
dc.descriptionWe calculate the local Green function for a quantum-mechanical particle with hopping between nearest and next-nearest neighbors on the Bethe lattice, where the on-site energies may alternate on sublattices. 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 is extended to derive an operator identity which maps the problem onto the case of only nearest-neighbor hopping. We find in particular that hopping between next-nearest neighbors leads to an asymmetric spectrum with additional van-Hove singularities.
dc.description16 pages, 7 figures; minor changes
dc.identifierhttps://arxiv.org/abs/cond-mat/0504637
dc.identifierhttp://arxiv.org/abs/cond-mat/0504637
dc.identifierAnn. Phys. (Leipzig) 14, 642 (2005)
dc.identifierdoi:10.1002/andp.200510152
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/26266
dc.subjectStrongly Correlated Electrons
dc.titleGreen functions for nearest- and next-nearest-neighbor hopping on the Bethe lattice
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