Machine Learning Discrete-Time Crystals

Machine learning has emerged as a transformative tool in the physical sciences, offering innovative approaches to complex problems across various domains. One significant challenge in condensed matter physics is the determination of order parameters, which are crucial for characterizing different phases but often difficult to identify due to the lack of prior knowledge of the symmetry breaking of the system. In this study, we employ an autoencoder-based machine learning framework to map out the phase diagram of periodically kicked spin models, which possess a discrete time crystal phase. By tracing the reconstruction loss in the output of the autoencoder, we are able to detect the phase transitions of discrete-time crystal without explicit input of the order parameters. The work demonstrates the efficacy of unsupervised machine learning methods applied to phase transitions in out-of-equilibrium many-body systems and paves the way to the autonomous discovery of novel quantum phases.