Precise Identification of Topological Phase Transitions with Eigensystem-Based Clustering

Abstract: Recent advances in machine learning have spurred new ways to explore and classify quantum phases of matter. We propose an \(\textit{Eigensystem-based}\) representation, combined with a Gaussian Mixture Model (GMM), to unsupervisedly cluster Hamiltonians into distinct topological phases with minimal feature engineering. The method identifies different topological phases without any prior knowledge, pinpoints phase boundaries with remarkable precision \(\sim\mathcal{O}(10^{-5})\), remains robust under moderate noise, and scales efficiently via a simple dimensionality-reduction step. The success of GMM offers a novel physical insight — each phase forms a well-separated multivariate Gaussian in a high-dimensional “Eigensystem space.” We illustrate the approach on several 1D lattice models, all achieving near 100\% accuracies.

Recommended citation: Yan, Xianquan, and Jian-Song Pan. “Precise Identification of Topological Phase Transitions with Eigensystem-Based Clustering,” 2025.
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