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A small value of the spin gap in quantum antiferromagnets with strongfrustration makes them susceptible to nominally small deviations from the idealHeisenberg model. One of such perturbations, the anisotropicDzyaloshinskii-Moriya interaction, is an important perturbation for the $S=1/2$kagome antiferromagnet, one of the current candidates for a quantum-disorderedground state. We study the influence of the DM term in a relatedone-dimensional system, the sawtooth chain that has valence-bond order in itsground state. Through a combination of analytical and numerical methods, weshow that a relatively weak DM coupling, $0.115J$, is sufficient to destroy thevalence-bond order, close the spin gap, and turn the system into a Luttingerliquid with algebraic spin correlations. A similar mechanism may be at work inthe kagome antiferromagnet.

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