Holstein-Primakoff Representation for Strongly Correlated Electron Systems

Abstract

First we show that the algebra of operators entering the Hamiltonian of the t-J model describing the strongly correlated electron system is graded spl(2.1) algebra. Then after a brief discussion of its atypical representations we construct the Holstein-Primako nonlinear realization of these operators which allows to carry out the systematic semiclassical approximation, similarly to the spin-wave theory of localized magnetism. The fact that the t-J model describes the itinerant magnetism is reflected in the presence of the spinless fermions.

For the supersymmetric spl(2.1) algebra the supercoherent states are proposed and the partition function of the t-J model is represented as a path integral with the help of these states.