Unsupervised identification of Floquet topological phase boundaries

TL;DR

This paper introduces an unsupervised machine learning method to identify phase boundaries in Floquet topological systems, leveraging system dynamics, adiabatic deformation, and symmetry to reveal complex nonequilibrium topological phases.

Contribution

The work presents a novel machine learning protocol that integrates dynamics, adiabatic deformation, and symmetry for topological phase classification in periodically driven systems.

Findings

Successfully identified phase boundaries in Floquet systems

Revealed complex topological phases inaccessible in static systems

Demonstrated robustness of the method across case studies

Abstract

Nonequilibrium topological matter has been a fruitful topic of both theoretical and experimental interest. A great variety of exotic topological phases unavailable in static systems may emerge under nonequilibrium situations, often challenging our physical intuitions. How to locate the borders between different nonequilibrium topological phases is an important issue to facilitate topological characterization and further understand phase transition behaviors. In this work, we develop an unsupervised machine-learning protocol to distinguish between different Floquet (periodically driven) topological phases, by incorporating the system's dynamics within one driving period, adiabatic deformation in the time dimension, plus the system's symmetry all into our machine learning algorithm. Results from two rich case studies indicate that machine learning is able to reliably reveal intricate topological phase boundaries and can hence be a powerful tool to discover novel topological matter afforded by the time dimension.