Amortized Clustering Assistant Classification of Anomalous Hybrid Floquet Modes in a Periodically Driven non-Hermitian Lattice

TL;DR

This paper introduces a machine learning approach to classify Floquet modes in a non-Hermitian lattice, revealing topological phases and dynamic localization effects under complex periodic driving.

Contribution

It develops an amortized clustering algorithm to efficiently analyze eigenfunctions and classify Floquet modes in a driven non-Hermitian system, advancing computational methods in topological physics.

Findings

Discovery of two nontrivial Floquet topological phases supporting {} modes

Development of an adaptive clustering algorithm for eigenfunction analysis

Revealing regulation of dynamic localization through machine learning

Abstract

The interplay between Floquet periodically driving and non-Hermiticity could bring about intriguing novel phenomena with anomalous Floquet topological phases of a finite-size, tight-binding lattice model. How to efficiently investigate on quasi-energy and eigenfield of a non-Hermitian Floquet system with complicated driving protocol remains a challenging task. In this work, we define a somewhat complex driving protocol for a bipartite lattice system and discover two nontrivial topological phases that support Floquet {\pi} mode. Thereafter, we introduce unsupervised learning method in order to explore distribution features of system eigenfunctions under different magnitude of system energy gain/loss. We utilize the idea of amortized clustering and construct an algorithm selector that could dynamically upgrade with increasing gain/loss as input parameter. Proper employment of the selector enables us to reveal the regulation of dynamic localization from abundant possible wave function distribution in two-dimension lattice in another efficient way. In addition, our work provides a feasible methodology via machine learning method to assist in classification of Floquet modes.