Hole dynamics in a strongly correlated two-dimensional spin background

In this paper we present results of finite-lattice studies of the t-J and the t-t'-J model for 18 (20) sites with up to 4 (2) holes. A modified Lanczos algorithm allowed for the classification of the ground state according to total spin S. In the one-hole sector we find evidence for the existence of hole pockets. We calculate the effective quasiparticle band and show qualitative differences between the t-J and t-t'-J model for J{}0.2. As U increases we notice a substantial band narrowing, which is maximal at the Nagaoka transition, accompanied by S-level crossings rendering a quasiparticle description difficult. In the high-doping regime we present hole binding energies for up to six holes for the t-J model. Evidence for phase separation is only found for J>t. We also studied the magnetic structure of the ground state on the 18-site lattice in the limit J=0. We present a complete ground-state classification for all numbers of holes Nₕ and find S=Sₘₐₓ at quarter filling in addition to the Nagaoka case.