Electron Hubbard Model

Ming-Yong Ye, Xiu‐Min Lin

Two‐dimensional Hubbard model is important to understand the high temperature superconductivity. We give several methods to construct exact eigenstates of the two‐dimensional Hubbard model that are independent of the on‐site electron interaction. The number of electrons in some eigenstates can be of the order of the lattice sites. It is shown that the existence of eigenstates independent of the electron interactions is a common feature of the extended Hubbard models that have short‐range interactions, and some eigenstates we construct can be used to represent eigenstates of the two‐dimensional Bose–Hubbard model.

Subir Sachdev A

Cary Mcilwaine Maguire

Edison A. Enaibe, Akpata Erhieyovwe, Nelson Oyindenyifa Nenuwe

The major characteristic of the single-band Hubbard model (HM) is to redistribute electrons at a uniform lattice separation distance within the molecular lattice. Hence, it is only linearly dependent on lattice separations distance. Thus the single-band Hubbard model does not consider the lattice gradient encountered by interacting electrons as they hop from one lattice point to another. The linear dependence of the single-band HM only on lattice separations would certainly not provide a thorough understanding of the interplay between interacting electrons. Consequently, we have in this study developed a gradient Hamiltonian model to solve the associated defects pose by the limitations of the single band Hubbard model. Thus, we utilized the single-band HM and the gradient Hamiltonian model to study the behaviour of two interacting electrons on a two dimensional (2D) 9X9 square lattice. It is revealed in this study that the results of the ground-state energies produced by the gradient Hamiltonian model are more favourable when compared to those of the single-band Hubbard model. We have also shown in this work, that the repulsive Coulomb interaction which in part leads to the strong electronic correlations, would indicate that the two electron system prefer not to condense into s-wave superconducting singlet state (s = 0), at high positive values of the interaction strength.

Sadulla Mamarazhabovich Tashpulatov

We consider a three-electron system in the Impurity Hubbard model with a coupling between nearest-neighbors.Our research aim consists of studying the structure of essential spectrum and discrete spectra of the energy operator of three-electron systems in the impurity Hubbard model in the quartet state of the system in a ν -dimensional lattice.We have reduced the study of the spectrum of the three-electron quartet state operator in the impurity Hubbard model to the study of the spectrum of a simpler operator.We proved the essential spectra of the three-electron systems in the Impurity Hubbard model in the quartet state is the union of no more than six segments, and the discrete spectrum of the system is consists of no more than four eigenvalues.