Spin wave self-energy calculations with vertex corrections
The spin wave self-energy function with vertex corrections is investigated in this paper using the spin polaron formulation. We implement the theory in the finite temperature (Matsubara) Green's function method in a representation where holes are described as spinless fermions and spins as normal bosons. The spins are characterized by hard-core bosonic operators in linear spin wave theory via the Holstein-Primakoff transformation. The hole-spin wave interaction in the spin polaron Hamiltonian is analogous to the conventional polaron problem and used as the interaction term in the S-matrix expansion. A general expression for the spin wave self-energy function is obtained by first determining the vertex corrections using the Feynman diagrammatic technique, and then evaluated all Matsubara frequency summations by contour integrations.