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Studying the MBL transition with neural networks: finite-size scaling and limits

Seminar über Theoretische Festkörperphysik


Hugo Théveniaut


24.06.2019 14:00


Room 10.01, 10th Floor, Bldg. 30.23, KIT Campus South


Laboratoire de Physique Théorique (LPT - IRSAMC), France


Dr. Elmer Doggen


Machine learning has recently been applied to condensed matter problems, for example inspiring new wave-functions ansatzes for variational methods or allowing for the discovery of new efficient Monte Carlo update schemes. In my talk, I will focus on its use for phase classification stimulated by the seminal paper of Carasquilla and Melko (Nature, 2017) that showed that a neural network can indeed predict accurately the critical temperature and exponents of the Ising transition, solely trained on low and high temperature spin configurations.

The discovery of a many-body localized phase (MBL) in quantum interacting systems with disorder has motivated a tremendous amount of work. The nature of the transition, its universality class as well as the existence of a many-body mobility edge or intermediate phases are still highly debated topics. I will present our study of the MBL transition in a prototypical spin model using neural networks. Our leitmotif was to produce quantitative predictions (as opposed to qualitative results often obtained in the community), with much care given to possible bias entering the analysis through the choice of input data, network architectures, etc.. I will also stress the limitations of this method. If time allows, I will present the results of a neural network analysis for a MBL transition in a two-dimensional lattice model.