Model Fractional Quantum Hall States on Lattices: Exact Parent Hamiltonians and Routes to Realization
Abstract
Recent advances in engineered quantum platforms have enabled the realization of bosonic Laughlin states at ν=1/2 and brought non-Abelian topological phases within experimental reach. A central theoretical challenge is to develop a unified framework connecting lattice fractional quantum Hall (FQH) model states, exact parent Hamiltonians, and experimentally accessible interactions. We systematically construct Hermitian parent Hamiltonians for which continuum lowest Landau level (LLL) model states sampled on lattice sites are exact zero modes. Using these model manifolds as quantitative references, we find that, within the projected lattice LLL at the flux densities studied, short-range density interactions stabilize Laughlin ground-state manifolds at ν=1/3 and 1/4, while two-body onsite repulsion supports a Moore--Read triplet at ν=1. Full multiband calculations reveal a sharp contrast: the Laughlin manifolds remain robust against interband mixing on the studied tori, whereas the Moore--Read triplet becomes less spectrally isolated and eventually undergoes a level crossing with competing states near the interband scale. Our framework provides a theoretical foundation for using lattice model states to guide the search for experimentally accessible Abelian and non-Abelian FQH states.
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BibTeX
@misc{ji2026model,
title = {{Model Fractional Quantum Hall States on Lattices: Exact Parent Hamiltonians and Routes to Realization}},
author = {Guangyue Ji and Jinjie Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25585},
eprint = {2609.25585},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25585},
}
RIS
TY - UNPB
TI - Model Fractional Quantum Hall States on Lattices: Exact Parent Hamiltonians and Routes to Realization
AU - Guangyue Ji
AU - Jinjie Zhang
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.25585
UR - https://arxiv.org/abs/2609.25585
AB - Recent advances in engineered quantum platforms have enabled the realization of bosonic Laughlin states at ν=1/2 and brought non-Abelian topological phases within experimental reach. A central theoretical challenge is to develop a unified framework connecting lattice fractional quantum Hall (FQH) model states, exact parent Hamiltonians, and experimentally accessible interactions. We systematically construct Hermitian parent Hamiltonians for which continuum lowest Landau level (LLL) model states sampled on lattice sites are exact zero modes. Using these model manifolds as quantitative references, we find that, within the projected lattice LLL at the flux densities studied, short-range density interactions stabilize Laughlin ground-state manifolds at ν=1/3 and 1/4, while two-body onsite repulsion supports a Moore--Read triplet at ν=1. Full multiband calculations reveal a sharp contrast: the Laughlin manifolds remain robust against interband mixing on the studied tori, whereas the Moore--Read triplet becomes less spectrally isolated and eventually undergoes a level crossing with competing states near the interband scale. Our framework provides a theoretical foundation for using lattice model states to guide the search for experimentally accessible Abelian and non-Abelian FQH states.
ER -