Fermionic systems with charge correlations

Abstract

In this paper, we show that a system of localized particles, satisfying the Fermi statistics and subject to finite-range interactions, can be exactly solved in any dimension. In fact, in this case it is always possible to find a finite closed set of eigenoperators of the Hamiltonian. Then, the hierarchy of the equations of motion for the Green's functions eventually closes and exact expressions for them are obtained in terms of a finite number of parameters. For example, the method is applied to the two-state model (equivalent to the spin-1/2 Ising model) and to the three-state model (equivalent to the extended Hubbard model in the ionic limit or to the spin-1 Ising model). The models are exactly solved for any dimension d of the lattice. The parameters are self-consistently determined in the case of d=1.

8 pages, to be published in Europhysics Letters

References in corpus (3)

• The Hubbard model within the equations of motion approach
• Equation of Motion Method for Composite Field Operators
• Composite operators and algebra constraints: a formalism for highly interacting systems

Cited by in corpus (14)

• One-dimensional extended Hubbard model in the atomic limit
• The extended Hubbard model in the ionic limit
• Diversity of charge orderings in correlated systems
• The Composite Operator Method (COM)
• Extended Hubbard model in the presence of a magnetic field
• Exact solution of the one-dimensional spin-$\frac{3}{2}$ Ising model in magnetic field
• Equations of motion approach to the spin-1/2 Ising model on the Bethe lattice
• New perspectives on the Ising model
• Exact solution of the 1D Hubbard model in the atomic limit with inter-site magnetic coupling
• Magnetic behavior of a spin-1 Blume-Emery-Griffiths model
• The magnetization plateaus of the ferro and anti-ferro spin-1 classical models with $S_z^2$ term
• Role of the attractive intersite interaction in the extended Hubbard model
• The high-temperature expansion of the classical Ising model with S_z^2 term
• Fermionic systems with charge correlations on the Bethe lattice