N\'eel and disordered phases of coupled Heisenberg chains with $S=1/2$ to S=4

TL;DR

This study investigates how frustration affects coupled Heisenberg chains with spins from 1/2 to 4, revealing gapless and gapped phases and the emergence of disordered states at maximal frustration.

Contribution

It extends previous S=1/2 analyses to higher spins, demonstrating the persistence of gapless and disordered phases across different spin magnitudes using advanced numerical methods.

Findings

Half-integer spins are gapless, behaving like a sliding Luttinger liquid.

Integer spins exhibit an intermediate disordered phase with a spin gap.

Disordered phase width correlates with the 1D Haldane gap.

Abstract

We use the two-step density-matrix renormalization group method to study the effects of frustration in Heisenberg models for $S=1/2$ to S=4 in a two-dimensional anisotropic lattice. We find that as in $S=1/2$ studied previously, the system is made of nearly disconnected chains at the maximally frustrated point, $J_d/J_{\perp}=0.5$, i.e., the transverse spin-spin correlations decay exponentially. This leads to the following consequences: (i) all half-integer spins systems are gapless, behaving like a sliding Luttinger liquid as in $S=1/2$; (ii) for integer spins, there is an intermediate disordered phase with a spin gap, with the width of the disordered state is roughly proportional to the 1D Haldane gap.