Machine learning phases of matter: Scalability and limitations

We present a scalable machine learning (ML) framework for distinguishing phases and identifying phase transitions in many-body systems. Scalability and transferability are central to the unprecedented computational efficiency of ML methods. In general, linear-scaling computation can be achieved through the divide and conquer approach, and the locality of physical properties is key to partitioning the system into sub-domains that can be solved individually. Our proposed ML framework for phase classification is similar in spirit to the Behle-Parrinello approach widely employed in ML-based quantum molecular dynamics simulations. We discuss the limitations of this approach and the important role of the correlation length. The prototypical two-dimensional Ising model is used to demonstrate the proposed framework. Implications for practical applications are also discussed.