Gapless spin liquid in the kagome Heisenberg antiferromagnet with Dzyaloshinskii-Moriya interactions

A preponderance of evidence suggests that the ground state of the nearest-neighbor $S=1/2$ antiferromagnetic Heisenberg model on the kagome lattice is a gapless spin liquid. Many candidate materials for the realization of this model possess in addition a Dzyaloshinskii-Moriya (DM) interaction. We study this system by tensor-network methods and deduce that a weak but finite DM interaction is required to destabilize the gapless spin-liquid state. The critical magnitude, ${D}_{c}/J\ensuremath{\simeq}0.012(2)$, lies well below the DM strength proposed in the kagome material herbertsmithite, indicating a need to reassess the apparent spin-liquid behavior reported in this system.