Destruction of valence-bond order in a $S=1/2$ sawtooth chain with a Dzyaloshinskii-Moriya term

TL;DR

This paper investigates how a small Dzyaloshinskii-Moriya interaction can destroy valence-bond order in a frustrated quantum spin chain, transforming it into a Luttinger liquid, with implications for kagome antiferromagnets.

Contribution

It demonstrates analytically and numerically that weak DM interactions can eliminate valence-bond order in a sawtooth chain, providing insights into similar effects in kagome antiferromagnets.

Findings

Weak DM coupling ($0.115J$) destroys valence-bond order

Spin gap closes and system becomes a Luttinger liquid

Implications for quantum-disordered ground states in frustrated magnets

Abstract

A small value of the spin gap in quantum antiferromagnets with strong frustration makes them susceptible to nominally small deviations from the ideal Heisenberg model. One of such perturbations, the anisotropic Dzyaloshinskii-Moriya interaction, is an important perturbation for the $S=1/2$ kagome antiferromagnet, one of the current candidates for a quantum-disordered ground state. We study the influence of the DM term in a related one-dimensional system, the sawtooth chain that has valence-bond order in its ground state. Through a combination of analytical and numerical methods, we show that a relatively weak DM coupling, $0.115J$, is sufficient to destroy the valence-bond order, close the spin gap, and turn the system into a Luttinger liquid with algebraic spin correlations. A similar mechanism may be at work in the kagome antiferromagnet.