Unsupervised learning of topological indices

I will present an unsupervised protocol for learning topological indices of quantum systems [1]. The idea is to produce ensembles of topologically equivalent data and then train a specially designed neural-network-based regressor for classifying them. The datasets of topologically equivalent samples are derived by continuously deforming some selected parent systems and this procedure does not require any knowledge of the topological numbers or how they are constructed. I will explicitly illustrate the protocol with two examples: It will be employed for classifying 1d band insulators in symmetry class AIII, characterized by a winding number, and 2d band insulators in symmetry class A, characterized by a Chern number.

[1] O. Balabanov and M. Granath, arXiv:1908.03469 (2019).