Refining Heuristic Predictors of Fractional Chern Insulators using Machine Learning
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917116446244864 |
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| author | Comas, Oriol Mayné i Fonseca, André Grossi Vaidya, Sachin Soljačić, Marin |
| author_facet | Comas, Oriol Mayné i Fonseca, André Grossi Vaidya, Sachin Soljačić, Marin |
| contents | We develop an interpretable, data-driven framework to quantify how single-particle band geometry governs the stability of fractional Chern insulators (FCIs). Using large-scale exact diagonalization, we evaluate an FCI metric that yields a continuous spectral measure of FCI stability across parameter space. We then train Kolmogorov-Arnold networks (KANs) -- a recently developed interpretable neural architecture -- to regress this metric from two band-geometric descriptors: the trace violation $T$ and the Berry curvature fluctuations $σ_B$. Applied to spinless fermions at filling $ν=1/3$ in models on the checkerboard and kagome lattices, our approach yields compact analytical formulas that predict FCI stability with over $>80 \%$ accuracy in both regression and classification tasks, and remain reliable even in data-scarce regimes. The learned relations reveal model-dependent trends, clarifying the limits of Landau-level-mimicking heuristics. Our framework provides a general method for extracting simple, phenomenological "laws" that connect many-body phase stability to chosen physical descriptors, enabling rapid hypothesis formation and targeted design of quantum phases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01873 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Refining Heuristic Predictors of Fractional Chern Insulators using Machine Learning Comas, Oriol Mayné i Fonseca, André Grossi Vaidya, Sachin Soljačić, Marin Strongly Correlated Electrons Disordered Systems and Neural Networks We develop an interpretable, data-driven framework to quantify how single-particle band geometry governs the stability of fractional Chern insulators (FCIs). Using large-scale exact diagonalization, we evaluate an FCI metric that yields a continuous spectral measure of FCI stability across parameter space. We then train Kolmogorov-Arnold networks (KANs) -- a recently developed interpretable neural architecture -- to regress this metric from two band-geometric descriptors: the trace violation $T$ and the Berry curvature fluctuations $σ_B$. Applied to spinless fermions at filling $ν=1/3$ in models on the checkerboard and kagome lattices, our approach yields compact analytical formulas that predict FCI stability with over $>80 \%$ accuracy in both regression and classification tasks, and remain reliable even in data-scarce regimes. The learned relations reveal model-dependent trends, clarifying the limits of Landau-level-mimicking heuristics. Our framework provides a general method for extracting simple, phenomenological "laws" that connect many-body phase stability to chosen physical descriptors, enabling rapid hypothesis formation and targeted design of quantum phases. |
| title | Refining Heuristic Predictors of Fractional Chern Insulators using Machine Learning |
| topic | Strongly Correlated Electrons Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2512.01873 |