DYNAMICS OF A SMALL DENSITY OF HOLES IN A 2-DIMENSIONAL QUANTUM ANTIFERROMAGNET

The hole dynamics in a quantum antiferromagnetic background for a smal l doping concentration is studied within the t-J model description. Th e noncrossing approximation for the hole self-energy is used. The corr ect quasiparticle pole structure (without artificial broadening) in th e spectral density function is employed. Dyson's equation for the hole Green's function is solved numerically by introducing a lattice in mo mentum space. The evolution of the density of states and the momentum- distribution function for holes is investigated as a function of hole- magnon coupling constant t at fixed J. The momentum distribution funct ion shows a sharp drop at the Fermi surface for several different hole -magnon coupling constants. This indicates the validity of the Fermi l iquid description for the t-J model in the low doping concentration. T he volume (surface) enclosed by the Fermi surface (curve) is found to be invariant for all the coupling strengths we have studied. The incoh erent spectrum below the chemical potential in the density of states b ecomes more significant for stronger interaction constants. These feat ures numerically verify Luttinger's theorem for a small density of dop ed holes in the t-J model. The optical conductivity is computed using the lowest-order diagrams. As the hole-magnon coupling constant t incr eases, absorption becomes stronger at omega congruent to 2J, the chara cteristic frequency for spin waves. This feature may be associated wit h the experimentally observed midinfrared absorption band in underdope d cuprates.