in the limit $U\rightarrow \infty $.

    The nonperturbative approach, presented in this paper, can, in principle, be applied to clusters of any size, as well as, to another types of model Hamiltonians.
author:
- |
    M.Matlak[^1], J.Aksamit, B.Grabiec\
    Institute of Physics, Silesian University,\
    4 Uniwersytecka, PL-40-007 Katowice,Poland\
    and\
    W.Nolting\
    Institute of Physics, Humboldt University,\
    110 Invalidenstr., D-10115 Berlin, Germany
title: 'Hubbard Hamiltonian in the dimer representation. Large $U$ limit'
---

Introduction
============

The single-band Hubbard model, Ref. \[1\], plays in the solid state physics a similar principal role as the hydrogen atom in the atomic physics. This explains a continuous interest in its properties. The Hubbard Hamiltonian reads $$H=\sum\limits_{i,j,\sigma }t_{i,j}c_{i,\sigma }^{+}c_{j,\sigma
}+U\sum\limits_in_{i,\uparrow }n_{i,\downarrow }.$$ Here $c_{i,\sigma }$ $(c_{i,\sigma }^{+})$ are annihilation (creation) operators of an electron with spin $\sigma =\uparrow $, $\downarrow $ in the Wannier representation at the lattice site $\mathbf{R}_i$ and $n_{i,\sigma
}=c_{i,\sigma }^{+}c_{i,\sigma }$. Moreover, $t_{i,j}$ is the hopping integral between different lattice sites $i$ and $j$ ($t_{i,i}=0)$ and $U$ is the intrasite Coulomb repulsion. The Bloch conduction band energy $%
\varepsilon _{\mathbf{k}}$ is given by

$$\varepsilon _{\mathbf{k}}=\sum\limits_{i-j}t_{i,j}e^{-i\mathbf{k\cdot (R}_i-%
\mathbf{R}_j)}.$$

In the following we restrict ourselves to the simple cubic (sc) lattice and assume that

$$t_{i,j}=\left\{ 
\begin{array}{ll}
