The representations of the Hubbard algebra in terms of spin-fermion operators and motion of a hole in an antiferromagnetic state

Abstract

The representation of the Hubbard operators in terms of the spin$-\frac{1}{2}$ operators and the fermion operator with spin$-\frac{1}{2}$ is proposed. In the low-energy limit this representation is reduced to the representation following from the Hubbard diagramm technique. In framework of this approach motion of a hole in an antiferromagnetic state of the t-J model is considered. It is shown that the primary hole energy is strongly renormalized and the band width has an order of J rather than t. The functional integral for the strongly correlated model induced by the obtained representation is formulated. The representation of the total Hubbard algebra for states in the lower and the upper Hubbard bands is formulated in terms of the spin$-\frac{1}{2}$ and two fermion fields with spin$-\frac{1}{2}$ is formulated.