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, with the transverse exchanges being irrelevant. This result is extended here to transverse couplings up to , 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 behaviour persists upon moderate hole doping . For larger doping, the frustration becomes inactive and the quantum critical point is suppressed.
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