Phase diagram of three-leg ladders at strong coupling along the rungs

TL;DR

This paper derives the phase diagram of a three-leg t-J ladder at strong rung coupling, revealing transitions between Luttinger liquid and Luther-Emery phases depending on the exchange coupling ratio and hole doping levels.

Contribution

It provides a detailed phase diagram for the three-leg ladder model at strong rung coupling, identifying critical points and phase transitions based on coupling ratios and doping.

Findings

Transition from Luttinger liquid to Luther-Emery liquid at high J_perp/t_perp

Sequence of three Luttinger liquid phases at lower J_perp/t_perp

Critical hole concentration approximately 1/3 for phase transition

Abstract

A phase diagram of the t-J three-leg ladder as a function of hole dopping is derived in the limit where the coupling parameters along the rungs, $t_{\perp}$ and $J_{\perp}$, are taken to be much larger than those along the legs, $t_{||}$ and $J_{||}$ At large exchange coupling along the rungs, $J_{\perp}/t_{\perp}> 3 / \sqrt{2}$, there is a transition from a low-dopping Luttinger liquid phase into a Luther-Emery liquid at a critical hole concentration $n_{crit}\approx 1/3$. In the opposite case, $J_{\perp}/t_{\perp}< 3 / \sqrt{2}$, there as a sequence of three Luttinger liquid phases (LLI, LLII and LLIII) as a function of hole dopping.