Hopping on the Bethe lattice: Exact results for densities of states and dynamical mean-field theory

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dc.creatorEckstein, Martin
dc.creatorKollar, Marcus
dc.creatorByczuk, Krzysztof
dc.creatorVollhardt, Dieter
dc.date2004-09-29
dc.date2005-07-23
dc.date.accessioned2026-07-07T03:01:05Z
dc.date.available2026-07-07T03:01:05Z
dc.descriptionWe derive an operator identity which relates tight-binding Hamiltonians with arbitrary hopping on the Bethe lattice to the Hamiltonian with nearest-neighbor hopping. This provides an exact expression for the density of states (DOS) of a non-interacting quantum-mechanical particle 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. These methods are based only on the so-called distance regularity of the infinite Bethe lattice, and not on the absence of loops. Results are also obtained for the triangular Husimi cactus, a recursive lattice with loops. Furthermore we derive the exact self-consistency equations arising in the context of dynamical mean-field theory, which serve as a starting point for studies of Hubbard-type models with frustration.
dc.description14 pages, 9 figures; introduction expanded, references added; published version
dc.identifierhttps://arxiv.org/abs/cond-mat/0409730
dc.identifierhttp://arxiv.org/abs/cond-mat/0409730
dc.identifierPhys. Rev. B 71, 235119 (2005)
dc.identifierdoi:10.1103/PhysRevB.71.235119
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/24953
dc.subjectStrongly Correlated Electrons
dc.titleHopping on the Bethe lattice: Exact results for densities of states and dynamical mean-field theory
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