UNITARY TRANSFORMATION TREATMENT OF A SINGLE HOLE IN AN ISING ANTIFERROMAGNET

The behavior of a single hole in a two-dimensional Ising antiferromagn et (t-J(z) model) is studied in the generalized Dyson-Maleev represent ation, where the spins are mapped on boson operators and the hole is d escribed as a spinless fermion. The formal similarity with Frohlich's polaron Hamiltonian suggests that the t-J(z) model can be approximatel y diagonalized by means of two successive unitary transformations, ana logous to those used by Lee, Low, and Pines in their intermediate-coup ling treatment of the polaron. Our approach yields an upper bound to t he exact ground state energy, as well as the corresponding ground stat e eigenvector. For k = 0 our energy bound is remarkably close to the r esult of the self-consistent Born approximation over a wide range of t he coupling parameter, which includes the range typically assumed for the high-T(c) materials. The ground state eigenvector is used to calcu late the spatial distribution of bosons (spin deviations) surrounding the hole. Here our results are qualitatively very similar to those obt ained in previous work, showing that our ground state eigenvector acco unts quite well for the small size of the ''spin polaron'' in the t-J( z) model.