SPIN AND CHARGE MODES OF THE t-J LADDER

TL;DR

This study investigates the spin and charge excitations in the t-J ladder model using exact diagonalization, revealing phases with hole pairing, spin gaps, and Luttinger liquid behavior depending on doping and interaction strength.

Contribution

It provides a detailed classification of modes and finite size scaling analysis, highlighting the emergence of superconducting correlations and phase transitions in the t-J ladder.

Findings

Hole pairing induces a spin gap at low doping.

Superconducting pairing correlations are linked to a charge bonding mode.

At higher doping, the system exhibits Luttinger liquid characteristics.

Abstract

The spin and charge excitations of the t--J ladder are studied by exact diagonalization techniques for several electron densities. The various modes are classified according to their spin (singlet or triplet excitations) and their parity under a reflection with respect to the symmetry axis along the chains and a finite size scaling of the related gaps is performed. At low doping, formation of hole pairs leads to a spin gap for all $J/t$ ratios. This phase is characterized by (at least) one vanishing energy mode {\it only} in the charge bonding channel when $K_x\rightarrow 0$ consistent with the existence of superconducting pairing correlations. At larger doping the spin gap disappears. Although the anti-bonding modes remain gapped, low energy $K_x\sim 0$ and $K_x\sim 2k_F$ spin and charge bonding modes are found consistent with a single band Luttinger scenario. At sufficient low electron density and above a critical value of J/t we also expect another phase of electron pairs with gapped spin excitations.