Non-Equilibrium Dynamics: Previous studies of topological effects have mostly focused on equilibrium or near-equilibrium situations. We show that the topological invariant can also manifest its physical effect in a quench dynamics far from equilibrium.

Interaction Effect: We utilize the recently proposed Sachdev-Ye-Kitaev model and construct an exactly solvable model to address the interaction effect in a topological band insulator. An interaction-induced topological transition and its critical behaviors can be shown explicitly by this model.

Machine Learning: We show that we can train a neural network to predict accurately a topological invariant from local input, and without human knowledge as a prior. We also analyze the neural network to show that what is captured by the neural network is precisely the mathematical formula for topological invariant.

References:

[1] Ce Wang, Pengfei Zhang, Xin Chen, Jinlong Yu, and Hui Zhai, Phys. Rev. Lett . 118 , 185701 (2017)

[2] Pengfei Zhang, Huitao Shen, and Hui Zhai, Phys. Rev. Lett . 120 , 066401 (2018)

[3] Pengfei Zhang and Hui Zhai, Phys. Rev. B 97 , 201112(R) (2018)