Exact Green's Function for the Bethe Lattice in the Hopping Model
Year: 2014
Type: article
Abstract: We calculated the exact self energy and the exact Green's function for the Bethe lattice in the hopping model using the Dyson's equation and from the fourth order of perturbation theory. The self energy is found from processes where an electron hops to its neighbors and includes terms where the particle hops twice to a next nearest neighbor (NNN) and then hops back. 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. In this study, the electron Green's function will be used to calculate the exact Green's function and self energy for the Bethe lattice in the hopping model. Though it is not one of the goals of our study here, it is pertinent to point out that the self energy can be used to obtain the vertex function which contains all the information on the kinetic and interaction behaviour of the particles in the system. Interestingly the vertex function can be decoupled into the charge vertex function and spin vertex function, thereby enabling the studying of either non-spin ordering systems or spin ordering system independently.
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W76282316