Path integral of Heisenberg model with thermal vacancies

Abstract

We construct the coherent-state path integral of the antiferromagnetic, Heisenberg model with thermal vacancies. We use the slave-boson method to account for the vacancies and the no-double occupancy constraint of the system. With the use of the Hubbard-Stratonovich transformation, we evaluate the path integral and derive the effective action. For a uniform resonating valence bond state on a square lattice, we obtain the spinon and boson dispersion relations and calculate the analytic form of the free energy.