Phase classification

Distinguishing between different phases of matter and detecting phase transitions are some of the most central tasks in many-body physics. Traditionally, these tasks are accomplished by searching for a small set of low-dimensional quantities capturing the macroscopic properties of each phase of the system, so-called order parameters. Because of the large state space underlying many-body systems, success generally requires a great deal of human intuition and understanding. In particular, it can be challenging to define an appropriate order parameter if the symmetry breaking pattern is unknown or the phase is of topological nature and thus exhibits nonlocal order. In this chapter, we explore the use of machine learning to automate the task of classifying phases of matter and detecting phase transitions. We discuss the application of various machine learning techniques, ranging from clustering to supervised learning and anomaly detection, to different physical systems, including the prototypical Ising model that features a symmetry-breaking phase transition and the Ising gauge theory which hosts a topological phase of matter.