Machine Learning In Disordered Systems

In this thesis we study phase transitions in interacting and non-interacting disordered systems by a combination of modern machine learning techniques and conventional methods.We start to establish a link between the two different approaches by questioning about the feature that machine extracts for distinguishing the phases.The question is explored using a simple feed forward neural network and a convolutional neural network.Our study on many-body localization transition reveals that feed forward neural network without a feature extractor is less efficient in learning the non-trivial physics,compared to convolutional neural network.With the latter,we successfully show that machine learning methods can discover physics quantity,such as nearest-neighbour and even further-neighbour level spacing,to distinguish the phases.In general our work provides a detailed example of how one may use machine learning to develop and to improve methods based on low-level data in disordered systems.We further apply machine learning techniques to study a disordered three-dimensional quantum Hall system,which features metal-insulator transitions in the bulk,as well as a quasi-one-dimensional metal-insulator crossover on the surface.On the one hand,we combine the study of level statistics with the Kullback-Leibler divergence as a new tool for phase detection.Using this tool,we not only map the phase diagram of a three-dimensional quantum Hall system but also explore the nature of its distinct surface states.On the other hand,we show that a convolutional neural network is capable of distinguishing bulk states from surface states even at a relatively small system size,hence locating the mobility edge separating metallic and quantized Hall insulating phases.We conclude that combining machine learning techniques and findings with conventional methods and insights can be fruitful in the study of disordered quantum systems.