Adversarial Domain Adaptation for Identifying Phase Transitions

The identification of phases of matter is a challenging task, especially in quantum mechanics, where the complexity of the ground state appears to grow exponentially with the size of the system. Traditionally, physicists have to identify the relevant order parameters for the classification of the different phases. We here follow a radically different approach: we address this problem with a state-of-the-art deep learning technique, adversarial domain adaptation. We derive the phase diagram of the whole parameter space starting from a fixed and known subspace using unsupervised learning. This method has the advantage that the input of the algorithm can be directly the ground state without any ad hoc feature engineering. Furthermore, the dimension of the parameter space is unrestricted. More specifically, the input data set contains both labeled and unlabeled data instances. The first kind is a system that admits an accurate analytical or numerical solution, and one can recover its phase diagram. The second type is the physical system with an unknown phase diagram. Adversarial domain adaptation uses both types of data to create invariant feature extracting layers in a deep learning architecture. Once these layers are trained, we can attach an unsupervised learner to the network to find phase transitions. We show the success of this technique by applying it on several paradigmatic models: the Ising model with different temperatures, the Bose-Hubbard model, and the Su-Schrieffer-Heeger model with disorder. The method finds unknown transitions successfully and predicts transition points in close agreement with standard methods. This study opens the door to the classification of physical systems where the phase boundaries are complex such as the many-body localization problem or the Bose glass phase.