Dynamics of Small Spin Polaron in the Three-Band Model of Two-Dimensional Spherically Symmetric Antiferromagnet

The retarded Green's function G(k,\omega) of a single small spin polaron in the three-band model for the CuO_2 plane is calculated in the self-consistent Born approximation. It is shown that such a spin polaron is a good quasiparticle excitation for realistic values of spin exchange J and effective hopping \tau. The polaron spectral density A_p(k,\omega) demonstrates small damping in contrast to the results of calculations starting from the bare hole, i.e. the pole strength of the energetically low-lying quasiparticle peak Z_p(k) varies from 50% to 82% for J/\tau ~ 0.1/0.7. The quasiparticle peak dispersion reproduces the main features of the bare polaron spectrum \Omega_k near the band bottom. The spherically symmetric approach is used for the description of spin excitations. It makes it possible to consider the quantum antiferromagnetic background without the spontaneous symmetry breaking and the unit cell doubling. The new method of the self-consistent calculation, based on continued fraction expansion of Green's function, is represented in details. The method preserves the proper analytical properties of the Green's function and provides the possibility to analyze the nature of its singularities.