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

TL;DR

This study explores the ground state properties of the anisotropic two-leg ladder $t-J$ model, revealing phase separation tendencies and the formation of tightly bound hole pairs through a cluster-based approach supported by numerical exact diagonalization.

Contribution

Introduces a cluster approach using 4-site plaquettes to analyze the $t-J$ model on a ladder, highlighting phase separation and hole pairing mechanisms.

Findings

Ground state energy well described by plaquettes with charges Q=2,4

Interaction favors condensation of maximal charge plaquettes, indicating phase separation

Numerical exact diagonalization supports the cluster approach

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 ($t',\alpha'=J'/t'$) along legs. We have implemented a cluster approach based on 4-site plaqettes. In the strong asymmetric cases $\alpha/\alpha'\ll 1$ and $\alpha'/\alpha\ll 1$ 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.