6533b871fe1ef96bd12d19dd
RESEARCH PRODUCT
Green functions for nearest- and next-nearest-neighbor hopping on the Bethe lattice
Krzysztof ByczukKrzysztof ByczukP. G. J. Van DongenVladimir DobrosavljevicMarcus KollarDieter VollhardtWalter MetznerMartin EcksteinGabriel KotliarD. TanaskovićM. H. Radke De CubaN. Blümersubject
PhysicsImplicit functionBethe latticeStrongly Correlated Electrons (cond-mat.str-el)Operator (physics)Spectrum (functional analysis)General Physics and AstronomyFOS: Physical sciencesPartition function (mathematics)01 natural sciences010305 fluids & plasmask-nearest neighbors algorithmCondensed Matter - Strongly Correlated Electrons0103 physical sciencesPath integral formulationGravitational singularityddc:530Condensed Matter::Strongly Correlated ElectronsStatistical physics010306 general physicsdescription
We 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2005-04-25 |