Topological Trio

Topological physics has been studied for more than three decades, can we still find something new ? In this talk I will present three answers from our recent work:
Non-Equlibirum Dynamics: Previous studies of topological effect are mostly focused on equilibrium or near equilibrium situation, here we will show that the topological invariant can also manifest its physical effect in a quench dynamics far from equilibrium.
Machine Learning: We show that we can train a neural network to accurately predict 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 same mathematical formula for topological invariant.
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 are shown explicitly by this model.