Abstract
We propose a finite-temperature phase diagram for the 2D spin-$1/2$ $J_1-J_2$ $XXZ$ antiferromagnet on the triangular lattice. Our analysis, based on a composite fermion representation, yields several phases. This includes a zero-temperature helical spin liquid with $N=6$ {\it 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 $120^\circ$ ordered state around $J_2/J_1\approx0.089$ 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.
Highlights
Two-dimensional (2D) s = 1/2 magnets with frustrated interactions attract a great deal of interest because of their potential to host unconventional states of quantum matter such as spin liquids (SLs) [1,2,3,4,5,6,7,8,9]
An advantage of the fermion representation is that it can be used to effectively describe both the ordered phases as Chern-Simons (CS) superconductors [30], and spin liquids, where the fermions can be “deconfined.” There are two main differences between our work and previous approaches to establish spin liquids: In our framework, we start by focusing on the ordered states of the spin-1/2 XXZ magnet via treating it as superconducting states of spinless Chern-Simons fermions
There are two main differences between our work and previous approaches to establish spin-liquids: In our framework, we start by focusing on the ordered states of the spin-1/2 XXZ magnet via treating it as superconducting states of spinless CS fermions
Summary
A finite vector chirality and the anisotropy of individual Dirac cones are the main properties of the proposed SL, dubbed here a helical SL, which may be detected using DMRG, tensor network, or variational Monte Carlo approaches. They may be observed in spin-resolved neutron scattering. This implies that noninteracting bosons can condense to any superposition of these two states, the hard-core interactions prevent forming a density modulation and enforce condensation into one of these two points This leads to the doubly degenerate ground states, identified with the planar 120◦ Néel configurations of spins with two helicities [Figs.
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