Unitary transformation treatment of a single hole in an Ising antiferromagnet

Abstract

The motion of a single hole in a two-dimensional Ising antiferromagnet ( t − J z model) is studied in a representation, where the spins are treated in the linear spin-wave approximation and the hole is described as a spinless fermion. The formal similarity with Fröhlich's polaron Hamiltonian suggests that the t − J z model can be approximately diagonalized by means of two successive unitary transformations, analogous to those used by Lee, Low, and Pines in their intermediate-coupling treatment of the polaron. The first one is the lattice version of the Jost transformation, and its effect on the Hamiltonian is that the latter becomes diagonal in the hole operators. The remaining pure boson part is then subject to a displaced-oscillator transformation to eliminate all terms linear in the boson operators. The resulting energy E(k) is a rigorous upper bound to the exact ground state energy and, for k = 0, compares well with analytic results based on the retraceable path approximation.