Unsupervised identification of Floquet topological phase boundaries

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. 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 paper, we develop an unsupervised machine-learning protocol to distinguish between different Floquet (periodically driven) topological phases possessed by theoretical models, 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 analyze and discover previously unknown topological phases afforded by the time dimension. As inspired by previous elegant methods in analyzing Floquet topological phases, one essential ingredient in our machine-learning approach is to directly investigate the system's evolution operators parametrized by time.