Quantum phase transition and sliding Luttinger liquid in coupled t-J chains

TL;DR

This paper investigates quantum criticality and Luttinger liquid behavior in coupled t-J chains with frustrated interactions, revealing a disordered ground state at maximal frustration and the persistence of this state under moderate doping.

Contribution

It extends previous findings on disordered ground states in frustrated coupled chains to higher transverse couplings and analyzes the effects of doping on quantum criticality.

Findings

Transverse spin correlations decay exponentially at maximal frustration.

Longitudinal correlations resemble those of decoupled chains.

Moderate doping preserves the disordered state, but higher doping suppresses quantum criticality.

Abstract

Using a recently proposed perturbative numerical renormalization-group algorithm, we explore the connection between quantum criticality and the emergence of Luttinger liquid physics in $t-J$ chains coupled by frustrated interactions. This study is built on an earlier finding that at the maximally frustrated point, the ground state of weakly-coupled Heisenberg chains is disordered, the transverse exchanges being irrelevant. This result is extended here to transverse couplings up to $J_{\perp}=0.6$, and we argue that it may also be valid at the isotropic point. A finite size analysis of coupled Heisenberg chains in the vicinity of the maximally frustrated point confirms that the transverse spin-spin correlations decay exponentially while the longitudinal ones revert to those of decoupled chains. We find that this behavior persists upon moderate hole doping $x \alt 0.75$. For larger doping, the frustration becomes inactive and the quantum critical point is suppressed.