Ground-State Properties of the $t$-$J$ Model for the CuO Double-Chain Structure

TL;DR

This study explores the ground-state properties of the $t$-$J$ model for CuO double-chains, revealing conditions favorable for superconductivity and characterizing the phase as a Luther-Emery liquid.

Contribution

It demonstrates how varying $J_1$ influences the ground state, showing antiferromagnetic $J_1$ promotes superconducting correlations in the double-chain structure.

Findings

Antiferromagnetic $J_1$ leads to Luther-Emery liquid behavior.

Superconducting pair correlations decay as power-law in the antiferromagnetic regime.

Ferromagnetic $J_1$ suppresses superconducting signatures.

Abstract

We investigate the ground-state properties of a correlated model for the double-chain structure in cuprates. We consider the $t$-$J$ model, in which the nearest-neighbor spin interaction $J_1$ is smaller than the next-nearest-neighbor interaction $J_2$ corresponding to the CuO double-chain structure. We vary $J_1$ from antiferromagnetic to ferromagnetic values and calculate the correlation functions including the superconducting pair correlation function. Employing the density-matrix renormalization group method, we show that the ground state for antiferromagnetic $J_1$ exhibits the hallmarks of the Luther-Emery liquid phase, in which the spin-singlet pair and charge-density-wave correlations exhibit power-law decays against distance, and the spin correlation function decays exponentially. Its signatures are gradually dismissed as $J_1$ approaches the ferromagnetic regime. Our findings suggest that the antiferromagnetic double-chain structure without ferromagnetic bonds is favorable for superconductivity.