Polaron-type transformations of the t– t′– J model

Abstract

The t– t′– J model at nearly half-filling is used to study the motion of holes in a two-dimensional square lattice with an antiferromagnetic order. The spin–charge separation concept is used and the t– J Hamiltonian is exactly mapped into the tensor-product space of holons and spin states with an exact elimination of redundant degrees of freedom. The linear spin wave approximation is used. The canonical transformation of the polaron theory is used to finally cast the Hamiltonian of the system in the form describing the interacting holon–magnon system. One magnon scattering processes are considered and the holon Green function is calculated in the self-consistent-Born-approximation. The equation for the self-energy is solved numerically. From the lowest energy peak of the spectral function the energies of quasi-particles, i.e., holons heavily dressed in magnons, are calculated.