The diagram theory for the degenerate two-orbital hubbard model

Abstract

We investigate the minimal model that takes orbital degrees of freedom into account: the degenerate twoorbital Hubbard model. Our consideration includes the intraatomic Coulomb interaction of two electrons with opposite spins on the same orbital and on different orbitals and interorbital hopping of tunneling electrons. We take the influence of states caused by Hund's rule coupling on the metal-insulator phase transition into account. We generalize the diagram theory developed for strongly correlated orbitally nondegenerate systems to the case of orbital degeneration. For the one-particle renormalized Green's function, we establish an equation of Dyson type for calculating the system spectral function using a simple approximation based on summing chain diagrams.We dedicate this paper to the memory of the outstanding Russian scientist and remarkable person Professor Sergei Vladimirovich Tyablikov, who departed us so early but whose papers and monographs [1], [2] left a deep footprint in science, contributing remarkably to the theory of magnetism, polaron theory, multiparticle physics, etc.With deep gratitude, we remember his considerable help in preparing scientific cadres for the Republic of Moldova. One of us (V. A. M.) experienced the tremendous charm of his remarkable personality firsthand. He was an example of kindness and principality and was demanding in science. His approval of someone's paper was always considered the highest endorsement.We shall remember him forever.

Diagram theory for the twofold-degenerate Anderson impurity model

“…The triplet states |9 , |10 and |11 are the lowest by energy. Quantum states enumerated above permit us to organize Hubbard transfer operators χ mn and establish the relation with fermion impurity operators [10]:…”

“…We use the perturbation theory elaborated previously for strongly correlated electron systems both of non degenerate [5][6][7][8][9][11][12][13][14] and of degenerate forms [10]. We study the process of renormalization of Green's function resulting from intra-and inter-orbital flips of tunneling electrons.…”

“…Our investigation is based on the diagram theory elaborated for strongly correlated electron systems as in non-degenerated [5][6][7][8][9][11][12][13][14]and as in twofold degenerated ones [10].…”

“…In the following the main ideas of the perturbation theory elaborated for non-degenerate strongly correlated systems are extended for degenerated systems. Such generalization has been discussed, for example, in the case of twofold degenerate Hubbard model [10]. As is known the new elements of this perturbation theory of strongly correlated systems are the irreducible correlation functions which contain all charge, spin and pairing quantum fluctuations.…”