Spin-orbit-locked symmetry and the stability of the triangular Dirac spin liquid in the ytterbium delafossites
Abstract
The Yb delafossites NaYbSe2, KYbSe2, CsYbSe2 and NaYbO2 are candidates for the triangular U(1) Dirac spin liquid, QED3 with Nf=4, but their exchange is spin-orbit coupled. Under their spin-orbit-locked space group we determine which operators the XXZ anisotropy and the bond-dependent couplings J±±, Jz± induce, and at what order. Symmetry forbids every Dirac mass, density and current at any order and, assuming adiabatic continuity, any new monopole term through charge three. At linear order the couplings reach only spin-2 members of the quartic multiplets 20' and 84, which share their dimensions with Heisenberg-allowed operators. At second order J±± and Jz± renormalize the anisotropy through Jz±2−2J±±2, and nine spin-1 quartics without Heisenberg partners appear, irrelevant at O(1/N). A single layer of a stable Heisenberg spin liquid thus acquires no relevant Lorentz-scalar operator from spin-orbit coupling. The Heisenberg liquid itself allows a Lorentz-vector 20' quartic of large-N dimension 2.92, with two-loop ε-expansion estimates 2.9-3.5. Rhombohedral stacking adds triplet-monopole tunneling between layers at first order. At the transition to 120∘ order the anisotropy is relevant, with crossover exponent yT≃0.74-1, and exact diagonalization shows that easy-plane anisotropy selects the chiral-Ising class. The out-of-plane spectrum at the K point then stays gapless, and the spin-flip to non-spin-flip ratio grows as ω−0.56 at leading order. Existing KYbSe2 neutron data below J do not fix the K-point exponent. In-plane fields induce a chiral mass and an out-of-plane moment proportional to sin3φ, zero along the bonds and canceling between CsYbSe2 layers, which the planar thermal Hall effect can test.
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BibTeX
@misc{iqbal2026spinorbitlocked,
title = {{Spin-orbit-locked symmetry and the stability of the triangular Dirac spin liquid in the ytterbium delafossites}},
author = {Yasir Iqbal},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04608},
eprint = {2611.04608},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04608},
}
RIS
TY - UNPB
TI - Spin-orbit-locked symmetry and the stability of the triangular Dirac spin liquid in the ytterbium delafossites
AU - Yasir Iqbal
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04608
UR - https://arxiv.org/abs/2611.04608
AB - The Yb delafossites NaYbSe_2, KYbSe_2, CsYbSe_2 and NaYbO_2 are candidates for the triangular U(1) Dirac spin liquid, QED_3 with N_f=4, but their exchange is spin-orbit coupled. Under their spin-orbit-locked space group we determine which operators the XXZ anisotropy and the bond-dependent couplings J_±±, J_z± induce, and at what order. Symmetry forbids every Dirac mass, density and current at any order and, assuming adiabatic continuity, any new monopole term through charge three. At linear order the couplings reach only spin-2 members of the quartic multiplets 20' and 84, which share their dimensions with Heisenberg-allowed operators. At second order J_±± and J_z± renormalize the anisotropy through J_z±^2−2J_±±^2, and nine spin-1 quartics without Heisenberg partners appear, irrelevant at O(1/N). A single layer of a stable Heisenberg spin liquid thus acquires no relevant Lorentz-scalar operator from spin-orbit coupling. The Heisenberg liquid itself allows a Lorentz-vector 20' quartic of large-N dimension 2.92, with two-loop ε-expansion estimates 2.9-3.5. Rhombohedral stacking adds triplet-monopole tunneling between layers at first order. At the transition to 120^∘ order the anisotropy is relevant, with crossover exponent y_T≃0.74-1, and exact diagonalization shows that easy-plane anisotropy selects the chiral-Ising class. The out-of-plane spectrum at the K point then stays gapless, and the spin-flip to non-spin-flip ratio grows as ω^−0.56 at leading order. Existing KYbSe_2 neutron data below J do not fix the K-point exponent. In-plane fields induce a chiral mass and an out-of-plane moment proportional to sin3φ, zero along the bonds and canceling between CsYbSe_2 layers, which the planar thermal Hall effect can test.
ER -