Resonantly interacting 2e/3 anyons: a controlled microscopic theory of anyon superconductivity
Abstract
We develop a microscopic theory of anyon superconductivity that connects electronic interactions in a lightly doped Laughlin state to the universal physics of a resonantly interacting anyon gas. Using geometric quantization of Laughlin quasiholes, we derive the effective many-body Hamiltonian of dilute charge-2e/3 anyons, including their valley structure, dispersion, and statistical and short-range interactions, together with an explicit map between anyon and electron observables. This reduces the dilute many-body problem to a few parameters fixed by data computable from few anyon numerics. In analogy with resonant Fermi and Bose gases, we organize the dilute anyon problem around a two-body binding resonance and its relevant and marginal perturbations. For a three-valley gas of charge-2e/3 anyons, we identify a resonance whose long-distance theory is governed by an Aharonov-Casher anyon Hamiltonian whose magnetic field is the statistical Chern-Simons field and whose ground state is exactly solvable. Using the ground state wavefunction, we demonstrate Cooper-pair off-diagonal long-range order directly in electron coordinates and determine the pairing symmetry and vortex-lattice structure. The leading perturbations at the fixed point are a relevant pair detuning and a marginal three-body contact in the valley-singlet channel, which determine the compressibility and sound velocity. A repulsive three-body coupling is marginally irrelevant, allowing the fixed point to control a parametrically broad dilute regime near pair resonance, while attractive three-body interactions instead generate charge-2e trimers. More broadly, our results show that binding thresholds between competing anyon composites host universal resonant regimes that are not captured by the lowest-energy anyon species alone, providing a new setting for controlled theories of anyon matter.
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BibTeX
@misc{li2026resonantly,
title = {{Resonantly interacting $2e/3$ anyons: a controlled microscopic theory of anyon superconductivity}},
author = {Qingchen Li and Pavel A. Nosov and Zhaoyu Han and Si-Yuan Chen and Taige Wang and Eslam Khalaf},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05529},
eprint = {2611.05529},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05529},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Resonantly interacting 2e/3 anyons: a controlled microscopic theory of anyon superconductivity
AU - Qingchen Li
AU - Pavel A. Nosov
AU - Zhaoyu Han
AU - Si-Yuan Chen
AU - Taige Wang
AU - Eslam Khalaf
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05529
UR - https://arxiv.org/abs/2611.05529
AB - We develop a microscopic theory of anyon superconductivity that connects electronic interactions in a lightly doped Laughlin state to the universal physics of a resonantly interacting anyon gas. Using geometric quantization of Laughlin quasiholes, we derive the effective many-body Hamiltonian of dilute charge-2e/3 anyons, including their valley structure, dispersion, and statistical and short-range interactions, together with an explicit map between anyon and electron observables. This reduces the dilute many-body problem to a few parameters fixed by data computable from few anyon numerics. In analogy with resonant Fermi and Bose gases, we organize the dilute anyon problem around a two-body binding resonance and its relevant and marginal perturbations. For a three-valley gas of charge-2e/3 anyons, we identify a resonance whose long-distance theory is governed by an Aharonov-Casher anyon Hamiltonian whose magnetic field is the statistical Chern-Simons field and whose ground state is exactly solvable. Using the ground state wavefunction, we demonstrate Cooper-pair off-diagonal long-range order directly in electron coordinates and determine the pairing symmetry and vortex-lattice structure. The leading perturbations at the fixed point are a relevant pair detuning and a marginal three-body contact in the valley-singlet channel, which determine the compressibility and sound velocity. A repulsive three-body coupling is marginally irrelevant, allowing the fixed point to control a parametrically broad dilute regime near pair resonance, while attractive three-body interactions instead generate charge-2e trimers. More broadly, our results show that binding thresholds between competing anyon composites host universal resonant regimes that are not captured by the lowest-energy anyon species alone, providing a new setting for controlled theories of anyon matter.
ER -