Generalized SYK models: non-Fermi Liquid and quantum chaos

The Sachdev-Ye-Kitaev (SYK) model is a concrete solvable model to study non-Fermi liquid properties and quantum chaos. I will discuss two generalizations of the SYK model that contains two SYK models with different number of Majorana modes. In the first model, they are coupled by quadratic terms and the solution shows a quantum phase transition between two non-Fermi liquid chaotic phases. In the second model, they are coupled by random interaction and we find the chaotic behavior could be tuned.