Green functions for nearest- and next-nearest-neighbor hopping on the Bethe lattice
Abstract
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.
Cite
@article{arxiv.cond-mat/0504637,
title = {Green functions for nearest- and next-nearest-neighbor hopping on the Bethe lattice},
author = {M. Kollar and M. Eckstein and K. Byczuk and N. Blümer and P. van Dongen and M. H. Radke de Cuba and W. Metzner and D. Tanaskovic and V. Dobrosavljevic and G. Kotliar and D. Vollhardt},
journal= {arXiv preprint arXiv:cond-mat/0504637},
year = {2007}
}
Comments
16 pages, 7 figures; minor changes