The extended Hubbard model in the ionic limit

Abstract

In this paper, we study the Hubbard model with intersite Coulomb interaction in the ionic limit (i.e. no kinetic energy). It is shown that this model is isomorphic to the spin-1 Ising model in presence of a crystal field and an external magnetic field. We show that for such models it is possible to find, for any dimension, a finite complete set of eigenoperators and eigenvalues of the Hamiltonian. Then, the hierarchy of the equations of motion closes and analytical expressions for the relevant Green's functions and correlation functions can be obtained. These expressions are formal because these functions depend on a finite set of unknown parameters, and only a set of exact relations among the correlation functions can be derived. In the one-dimensional case we show that by means of algebraic constraints it is possible to obtain extra equations which close the set and allow us to obtain a complete exact solution of the model. The behavior of the relevant physical properties for the 1D system is reported.

19 pages, 9 figures, 16 panels

References in corpus (8)

• Superconductivity mediated by charge fluctuations in layered molecular crystals
• The Hubbard model within the equations of motion approach
• Charge ordering and antiferromagnetic exchange in layered molecular crystals of the theta type
• Metal-insulator transition and charge ordering in the extended Hubbard model at one-quarter filling
• Universality of residence-time distributions in non-adiabatic stochastic resonance
• CPA for charge ordering in the extended Hubbard model
• Fermionic systems with charge correlations
• New perspectives on the Ising model

Cited by in corpus (18)

• One-dimensional extended Hubbard model in the atomic limit
• Charge orderings in the atomic limit of the extended Hubbard model
• Geometrical frustration of an extended Hubbard diamond chain in the quasi-atomic limit
• Diversity of charge orderings in correlated systems
• Exact solution of the one-dimensional spin-$\frac{3}{2}$ Ising model in magnetic field
• Extended Hubbard model in the presence of a magnetic field
• The effects of the next-nearest-neighbour density-density interaction in the atomic limit of the extended Hubbard model
• Equations of motion approach to the spin-1/2 Ising model on the Bethe lattice
• Low temperature pseudo-phase transition in an extended Hubbard diamond chain
• Unusual low-temperature behavior in the half-filled band of the one-dimensional extended Hubbard model in atomic limit
• Different orderings in the narrow-band limit of the extended Hubbard model on the Bethe lattice
• Spin and charge orderings in the atomic limit of the U-V-J model
• Quantum Otto engine mimicking Carnot near pseudotransitions in the one-dimensional extended Hubbard model in the atomic limit
• Generalization of Lieb-Wu wave function inspired by one-dimensional ionic Hubbard model
• Role of the attractive intersite interaction in the extended Hubbard model
• Waterlike density anomaly in fermions
• Fermionic systems with charge correlations on the Bethe lattice
• A class of solvable models in Condensed Matter Physics