Binding of holes and competing spin-charge order in simple and extended Hubbard model on cylindrical lattice: An exact diagonalization study

TL;DR

This study uses exact diagonalization to explore how hole binding and spin-charge order emerge in the Hubbard model on a cylindrical lattice, revealing how nonlocal interactions influence pairing and phase separation.

Contribution

It provides a detailed microscopic analysis of hole binding mechanisms and competing orders in the Hubbard model with both local and nonlocal interactions, using exact diagonalization.

Findings

Weak hole pairing mediated by magnetic correlations at intermediate U.

Attractive V induces multi-hole clustering and phase separation.

Repulsive V stabilizes charge-density-wave order coexisting with bound pairs.

Abstract

We investigate the binding of holes and the emergence of competing spin-charge order in the simple and extended Hubbard model using exact diagonalization on the 3x4 cylindrical lattice. For the simple Hubbard model (V=0), we find weakly bound hole pairing mediated by magnetic correlations at intermediate repulsive U, without any evidence of phase separation. Introducing nearest-neighbor interaction V reveals a rich phase diagram: attractive V drives multi-hole clustering and phase separation with localized magnetic quenching, while repulsive V stabilizes charge-density-wave (CDW) order that coexists with bound hole pairs within a modulated magnetic background. At strong coupling (U=10), the competition sharpens, with attractive V overcoming on-site repulsion to form magnetically quenched clusters and repulsive V producing robust CDW order that constrains pairing. Real-space analysis of spin and charge correlations provides microscopic evidence of distinct binding mechanisms -- phase separation versus correlation-mediated pairing -- depending on the sign and strength of intersite interaction V . Our results establish a comprehensive picture of how nonlocal Coulomb interactions reshape the landscape of hole-binding and collective order in correlated electron systems.