Machine Learning Vortices in the XY Model

Supervised machine learning algorithms can easily classify symmetry-broken phases in classical statistical physics. In this talk, I will discuss steps towards learning unconventional phase transitions driven by the emergence of topological defects. I will focus on the 2D XY model which exhibits a Kosterlitz-Thouless transition due to vortex-antivortex unbinding. Specifically, I will talk about a custom network architecture that (theoretically) can detect topological effects. For small lattice sizes, I claim that learning about vortices typically hinders the performance of a learning algorithm. For larger lattices, I will discuss some of the challenges of learning about vortices with artificial neural networks.