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arXiv · 2607.19466

Anyon Crystals and Hall Crystals in a Periodic Potential

Sayak Bhattacharjee·Julian May-Mann·Srinivas Raghu
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Abstract

We obtain integer and fractional quantum Hall crystals as ground states of a two-dimensional electron system subject to a strong perpendicular magnetic field and a periodic potential. For certain fractional states, we show that the Hall crystal can constitute an anyon crystal, with a periodic ordering of well-defined anyons. We find that the latter states can be stabilized at odd denominator Landau level filling fractions when Landau level mixing is sufficiently weak, and near half-filling of the underlying lattice. These phases are obtained from a mean-field analysis of an effective lattice model of bosons attached to an odd number of flux quanta, which transmutes their statistics to that of electrons. In boson coordinates, the Hall crystal is a supersolid: a superfluid with charge order. Under strong interactions, vortex-anti-vortex pairs spontaneously nucleate in the supersolid, realizing a crystalline state of anyons.

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Sayak Bhattacharjee, Julian May-Mann, Srinivas Raghu. 2026-07-21. Anyon Crystals and Hall Crystals in a Periodic Potential. https://arxiv.org/abs/2607.19466

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