Detecting topological order in Kitaev spin liquids using interpretable machine learning

Much attention has been brought to the rich phase diagram of the honeycomb Kitaev model, which hosts both gapped and gapless Z2 spin liquids in the exactly solvable regime. Here we ask the question: can data-driven techniques be used to discover features governing phase transitions away from the solvable point of the Kitaev model? We approach DMRG ground states from a quantum measurement perspective and take snapshots by repeatedly sampling projective measurements. We train an interpretable neural network architecture, the correlator convolutional neural network [1], to discern characteristic features of different phases [2]. The network is designed to process n-point functions of the spin degrees of freedom, picking out the most relevant terms that can be used to distinguish phases. We finally interpret the correlation functions learned by the neural network and relate them to existing understanding of the studied phases.

[1] C. Miles, A. Bohrdt, R. Wu, C. Chiu, M. Xu, G. Ji, M. Greiner, K. Q. Weinberger, E. Demler, E.-A. Kim, Nat. Comm. 12 3905 (2021)

[2] S. Feng, Y. He, N. Trivedi, Phys. Rev. A 106, 042417 (2022)