Numerical diagonalization studies of the t-J model with one and two holes on a 32-site square lattice

The t-J model is believed to be one of the simplest strong-coupling model of the low-energy physics of the anomalous metallic state of high-temperature superconductors. Understanding how the holes interact in this model is an important but difficult task. Numerical diagonalization is an important tool in this study. However, its major deficiency is the finite-size effects -- system sizes solvable using this method is severely limited. Previous studies of the t-J model were mostly limited to square clusters with no more than 26 sites. Recently, we are able to solve the t-J model on a 32-site square cluster with up to two holes. This 32-site cluster has the full rotational symmetry of the square lattice, and has more allowed wavevectors along the high symmetry directions in the Brillouin zone. In the one-hole model, we calculate the spin texture around the hole, and the full spectral function. In the two-hole model, we study the behavior of the holes at various J/t. By studying the model with one and two holes on the same geometry, we can have a systematic understanding of the interaction of the holes moving in the spin background.