Formation of clusters in the ground state of the $t-J$ model on a two leg ladder

Abstract

We investigate the ground state properties of the $t-J$ model on a two leg ladder with anisotropic couplings ($t,\alpha =J/t$) along rungs and ($t^{\prime },{\alpha }^{\prime }=J^{\prime }/t^{\prime }$) along legs. We have implemented a cluster approach based on 4-site plaqettes. In the strong asymmetric cases $\alpha /{\alpha }^{\prime }\ll 1$ and ${\alpha }^{\prime }/\alpha \ll 1$ the ground state energy is well described by plaquette clusters with charges $Q=2,4$. The interaction between the clusters favours the condensation of plaquettes with maximal charge -- a signal for phase separation. The dominance of Q=2 plaquettes explains the emergence of tightly bound hole pairs. We have presented the numerical results of exact diagonalization to support our cluster approach.

11 pages, 9 figures, RevTex4