Exploring Fractional Quantum Hall States with Deep Learning: From Abelian to Non-Abelian Phases
Abstract
Fractional quantum Hall systems host strongly correlated topological phases with potential applications in topological quantum computation, yet identifying their microscopic ground states remains challenging because competing phases are often nearly degenerate and Landau-level mixing is difficult to treat. Here, we introduce a symmetry-adapted neural-network wavefunction that describes Abelian and non-Abelian states while incorporating all Landau levels. The method accurately captures composite-fermion liquids and the emergence of Wigner crystallization at low filling. When the first Landau level is partially filled, finite-size overlaps and entanglement spectra provide evidence consistent with 2̅k1k+1-type parton phases at ν=4/3 and 7/5, while the ν=3/2 state exhibits anti-Pfaffian-like entanglement structure. These results demonstrate that neural-network wavefunctions offer a flexible framework for studying competing topological orders in fractional quantum Hall systems.
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BibTeX
@misc{ma2026exploring,
title = {{Exploring Fractional Quantum Hall States with Deep Learning: From Abelian to Non-Abelian Phases}},
author = {Xiangyu Ma and Kehuang Chen and Yuntian Gu and Weiluo Ren and Ji Chen and Di Luo and Fengcheng Wu and Xiang Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38533},
eprint = {2610.38533},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38533},
}
RIS
TY - UNPB
TI - Exploring Fractional Quantum Hall States with Deep Learning: From Abelian to Non-Abelian Phases
AU - Xiangyu Ma
AU - Kehuang Chen
AU - Yuntian Gu
AU - Weiluo Ren
AU - Ji Chen
AU - Di Luo
AU - Fengcheng Wu
AU - Xiang Li
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38533
UR - https://arxiv.org/abs/2610.38533
AB - Fractional quantum Hall systems host strongly correlated topological phases with potential applications in topological quantum computation, yet identifying their microscopic ground states remains challenging because competing phases are often nearly degenerate and Landau-level mixing is difficult to treat. Here, we introduce a symmetry-adapted neural-network wavefunction that describes Abelian and non-Abelian states while incorporating all Landau levels. The method accurately captures composite-fermion liquids and the emergence of Wigner crystallization at low filling. When the first Landau level is partially filled, finite-size overlaps and entanglement spectra provide evidence consistent with 2̅^k1^k+1-type parton phases at ν=4/3 and 7/5, while the ν=3/2 state exhibits anti-Pfaffian-like entanglement structure. These results demonstrate that neural-network wavefunctions offer a flexible framework for studying competing topological orders in fractional quantum Hall systems.
ER -