Exact diagonalisation 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 quasi-particule weight vanishes in the strong correlation limit $J\rightarrow 0$ while the quasi-particle mass diverges (like 1/J). However, the spectral function shows weight distributed over a large energy range ($\sim 7\, t$) 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 $\sqrt{26}\times\sqrt{26}$ cluster indicates that in the range $J/t\in [0.16,0.45]$ 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 $J/t|_{B,4}\sim 0.45$ the 2-holes pairs bind into 4-holes pairs. An abrupt change of the orbital symmetry of the 4-hole droplet is also observed above $J/t\sim 2.7$. 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.