EXACT DIAGONALIZATION STUDIES OF STRONGLY CORRELATED 2D LATTICE FERMIONS

The T=0 phase diagram of the planar t-J model with small doping is investigated by exact diagonalisations of square clusters with up to 32 sites. At half-filling, the single hole qaasi-particule weight vanishes in the strong correlation limit J --> 0 while the quasi-particle mass diverges (like 1/J). However, the spectral function shows weight distributed over a large energy range (similar to 7t) and a pronounced structure in momentum space which supports the composite particle picture of the hole. For J/t > J/t\(B,2) the effective attractive force between holes leads to bound-pairs formation. The hole-hole and hole pair-hole pair binding energies calculated on the root 26 x root 26 cluster indicates that in the range J/t is an element of [0.16,0.45] a phase of separate pairs of d-wave internal symmetry is stable. On the other hand, the d-wave pair spectral function exhibits a quasi-particle peak down to very small J/t ratios suggesting that J/t\(B,2) could in fact be as small as 0.05. Above J/t\(B,4) similar to 0.45 the 2-holes pairs bind into 4-holes pairs. An abrupt change of the orbital symmetry of the Q-hole droplet is also observed above J/t similar to 2.7. In the parameter range, J/t\(B,2) < J/t < J/t\(B,4,) Bose condensation of the individual pairs is expected to lead to d-wave superconductivity.