Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2004-09-29
Phys. Rev. B 71, 235119 (2005)
Physics
Condensed Matter
Strongly Correlated Electrons
14 pages, 9 figures; introduction expanded, references added; published version
Scientific paper
10.1103/PhysRevB.71.235119
We 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.
Byczuk Krzysztof
Eckstein Martin
Kollar Marcus
Vollhardt Dieter
No associations
LandOfFree
Hopping on the Bethe lattice: Exact results for densities of states and dynamical mean-field theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Hopping on the Bethe lattice: Exact results for densities of states and dynamical mean-field theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hopping on the Bethe lattice: Exact results for densities of states and dynamical mean-field theory will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-23367