Anyon Chern bands of opposite sign and reversed drift
Abstract
The elementary charged excitations of fractional quantum Hall states are anyons. Without continuous translation symmetry, they acquire a dispersion and richer dynamics. We study the Laughlin quasihole at filling 1/3 in a periodically modulated magnetic field, a common model of fractional Chern insulators in two-dimensional materials. From the microscopic wave functions, we derive the commutator of its guiding-center coordinates, set by a many-body Berry curvature that governs its wave packets. A modulation with two flux quanta per unit cell splits the quasihole band into bands with Chern numbers $6$ and −3; such opposite signs are generic as long as a weak modulation opens a gap between the anyon bands. In the C=−3 band, the quasihole drifts against E×B, although the magnetic field has the same sign everywhere. Perturbation theory in the modulation explains these results, and large-scale Monte Carlo calculations confirm them. Anyon bands thus acquire their own topology, which controls anyon motion and may shape the phases of itinerant anyons.
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BibTeX
@misc{xiao2026anyon,
title = {{Anyon Chern bands of opposite sign and reversed drift}},
author = {Zhenyu Xiao and Minxuan Wang and Shinsei Ryu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30743},
eprint = {2610.30743},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30743},
}
RIS
TY - UNPB
TI - Anyon Chern bands of opposite sign and reversed drift
AU - Zhenyu Xiao
AU - Minxuan Wang
AU - Shinsei Ryu
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.30743
UR - https://arxiv.org/abs/2610.30743
AB - The elementary charged excitations of fractional quantum Hall states are anyons. Without continuous translation symmetry, they acquire a dispersion and richer dynamics. We study the Laughlin quasihole at filling 1/3 in a periodically modulated magnetic field, a common model of fractional Chern insulators in two-dimensional materials. From the microscopic wave functions, we derive the commutator of its guiding-center coordinates, set by a many-body Berry curvature that governs its wave packets. A modulation with two flux quanta per unit cell splits the quasihole band into bands with Chern numbers $6$ and −3; such opposite signs are generic as long as a weak modulation opens a gap between the anyon bands. In the C=−3 band, the quasihole drifts against E×B, although the magnetic field has the same sign everywhere. Perturbation theory in the modulation explains these results, and large-scale Monte Carlo calculations confirm them. Anyon bands thus acquire their own topology, which controls anyon motion and may shape the phases of itinerant anyons.
ER -