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arXiv · 2610.40657

Variational wavefunctions for ideal anyon gas: superfluid and skyrmion Hall crystal

Ya-Hui Zhang
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Abstract

The ground state of an ideal gas of anyons with statistical angle $θ\in(0,π)$ is a long-standing open problem, with renewed interest from the recent observations of fractional Chern insulators. In this work we construct variational wavefunctions that build in the exact anyon statistics and combine theory-guided composite-boson, composite-fermion and parton wavefunctions with neural-network correlations on the sphere. For spinless and SU(2) semions we confirm the paired anyon superfluid, well below the best crystal states. At $θ=π/3$ liquids and crystals are closer in energy for the spinless case. For $θ=π/3$ anyons with SU(3) flavor, we find two candidates. One is a skyrmion Hall crystal, in which the anyons form an integer quantum Hall state in the effective magnetic field from the spin texture. The other is a chiral color superconductor of six-anyon clusters, the color-flavor-locked pairing descendant of a holon metal with SU(3) color gauge symmetry and SU(3) flavor symmetry; its wavefunction is a hyperdeterminant rather than a product of parton determinants. Within our variational ansatz the color superconductor has better energy than both crystals and the color-flavor locked phases with U(1)$^2$ and Z$_3$ gauge groups. For twisted MoTe$_2$ this suggests that the reentrant integer quantum anomalous Hall phase is the skyrmion Hall crystal of the doped anyons, and that the observed superconductivity may be the color superconductor, which can undergo a transition to an $f+if$ BCS superconductor with a jump of the chiral central charge by 3.

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Ya-Hui Zhang. 2026-10-29. Variational wavefunctions for ideal anyon gas: superfluid and skyrmion Hall crystal. https://arxiv.org/abs/2610.40657

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