The finite temperature Green's function method for the spin polaron problem

Abstract

In a past paper on spin polarons, the motion of a single hole in a two-dimensional Heisenberg antiferromagnet was analyzed based on the t-J model. Holes were described as spinless fermions (holons) and spins were treated as normal bosons (spinons). Using the linear spin-wave theory, spin dynamics was discussed with the assumption of long range antiferromagentic order, thereby closely resembling the conventional polaron problem. Using finite-cluster geometries for the numerical solution, the holon Green's function was calculated self-consistently within the Born approximation. The results revealed that even in the strong coupling regime, the formulation of the dynamics of a holon in the t-J model was quite valuable; in fact, a complete characterization was obtained, including a dispersion relation, the spectral weight, and the effective mass of the quasiparticle state.
In this paper, we shall treat the spin polaron problem using the finite temperature Green's function method (Matsubara method), as a possible mechanism for high temperature superconductivity, which in other previous works, is treated via mean-field method. We derive the spin-polaron interaction Hamiltonian based on the slave-fermion formulation. Dyson's equations were subsequently obtained along with the expression of the thermodynamic potential using the linked cluster expansion.