Spin Polarons in Two-Dimensional Systems

The problem of motion of holes on a square lattice of antiferromagnetically ordered spins is considered. An overview of the theory of hole dynamics in the antiferromagnetic background is presented. Motion of a single hole is rather well understood both by numerical and analytical methods. For small but finite concentration of holes a treatment analogous to the standard polaron theory is discussed starting with an exact mapping of the t-J Hamiltonian into holon and pseudospin variables.