Unsupervised Topological Phase Discovery in Periodically Driven Systems via Floquet-Bloch State

TL;DR

This paper introduces an unsupervised machine learning approach that analyzes Floquet-Bloch eigenstates to classify and discover non-equilibrium topological phases in periodically driven systems without prior knowledge of topological invariants.

Contribution

It presents a data-driven, kernel-based framework that directly extracts topological features from eigenstates, overcoming limitations of traditional analytical methods.

Findings

Successfully identifies topological invariants in various symmetry classes.

Robustly detects both 0-gap and π-gap topologies.

Applicable to complex non-equilibrium topological phases.

Abstract

Floquet engineering offers an unparalleled platform for realizing novel non-equilibrium topological phases. However, the unique structure of Floquet systems, which includes multiple quasienergy gaps, poses a significant challenge to classification using conventional analytical methods. We propose a novel unsupervised machine learning framework that employs a kernel defined in momentum-time ($\boldsymbol{k},t$) space, constructed directly from Floquet-Bloch eigenstates. This approach is intrinsically data-driven and requires no prior knowledge of the underlying topological invariants, providing a fundamental advantage over prior methods that rely on abstract concepts like the micromotion operator or homotopic transformations. Crucially, this work successfully reveals the intrinsic topological characteristics encoded within the Floquet eigenstates themselves. We demonstrate that our method robustly and simultaneously identifies the topological invariants associated with both the $0$-gap and the $\pi$-gap across various symmetry classes (1D AIII, 1D D, and 2D A), establishing a robust methodology for the systematic classification and discovery of complex non-equilibrium topological matter.