Refining Heuristic Predictors of Fractional Chern Insulators using Machine Learning

TL;DR

This paper introduces an interpretable machine learning framework that predicts the stability of fractional Chern insulators based on band geometry descriptors, improving understanding and design of quantum phases.

Contribution

It develops a data-driven, interpretable neural network approach to quantify and predict FCI stability from band geometric features, revealing model-dependent trends and limitations of existing heuristics.

Findings

Achieves over 80% accuracy in predicting FCI stability.

Provides analytical formulas linking band geometry to FCI stability.

Remains reliable in data-scarce regimes.

Abstract

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 $\sigma_B$. Applied to spinless fermions at filling $\nu=1/3$ 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.