We propose a finite-temperature phase diagram for the two-dimensional spin-$1/2$ $J_1-J_2$ XXZ antiferromagnet on a triangular lattice. Our analysis, based on a composite fermion representation, yields several phases. This includes a zero-temperature helical spin liquid with $N=6$ anisotropic Dirac cones, and with nonzero vector chirality implying a broken ${\mathbb{Z}}_2$ symmetry. It is terminated at $T=0$ by a continuous quantum phase transition to a ${120}^{\circ }$ ordered state around $J_2/J_1\approx 0.089$ in the XX limit; these phases share a double degeneracy, which persists to finite $T$ above the helical spin liquid. By contrast, at $J_2/J_1\simeq 0.116$, the transition into a stripe phase appears as first order. We further discuss experimental and numerical consequences of the helical order and the anisotropic nature of the Dirac dispersion.

• Received 6 December 2019
• Revised 3 July 2020
• Accepted 6 July 2020

DOI:https://doi.org/10.1103/PhysRevB.102.024430

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

Published by the American Physical Society