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arXiv · 2610.29278

Chirality, Klein duality, and the stability of Kitaev spin liquids on the star lattice

Harsh Raj·Yasir Iqbal
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Abstract

The star lattice hosts the Yao-Kivelson chiral spin liquid, an exactly solvable Kitaev spin liquid that breaks time reversal spontaneously and is non-Abelian or Abelian depending on the ratio of its two couplings. A density-matrix renormalization group study found that an added Heisenberg exchange leaves it a wide stability window for ferromagnetic but only a narrow one for antiferromagnetic Kitaev coupling. Using projective symmetry groups (PSGs) of fermionic partons, we show that the chirality is not a peculiarity of the solvable point: whenever the $π$ spin rotations act on the partons as in the exact solution (spin-gauge locking), a time-reversal-symmetric mean-field state has no amplitude on the triangles, at any range, so a Kitaev-type spin liquid on this lattice must break time reversal. The Abelian and non-Abelian liquids of both signs share a single chiral PSG, within which their transition is a band inversion. The Klein duality, which reverses the Heisenberg coupling, permutes the PSGs and leaves exactly the locked ones unchanged; a $Z_2$ spin-liquid phase mapped onto itself is therefore locked and, if it spans a connected range of couplings, contains a Kitaev point. Unprojected mean-field theory in Kitaev's Majorana representation treats both signs alike. Exact second-order perturbation theory about the Kitaev points locates the asymmetry: the triangles respond identically for both signs, whereas on the bonds between triangles the two off-diagonal Heisenberg terms create the same four visons and interfere constructively for antiferromagnetic and almost destructively for ferromagnetic coupling, admixing a low-energy four-vison state $82$ times more strongly on the antiferromagnetic side. The PSG results rest on a classification of $352$ $Z_2$ PSGs with spin-orbit-coupled amplitudes, which also identifies the fermionic partners of the known Schwinger-boson spin liquids.

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Harsh Raj, Yasir Iqbal. 2026-10-21. Chirality, Klein duality, and the stability of Kitaev spin liquids on the star lattice. https://arxiv.org/abs/2610.29278

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