Scrambling in Hyperbolic Ising Model

In this talk, we will investigate scrambling and chaos in the Hyperbolic Ising model. This model can be thought of as an Ising model that lives in an AdS2 background and the effects of the curved background are captured via site-dependent couplings obtained through the discretization of the background metric. To investigate chaos and information propagation in this model, we will first calculate Krylov-complexity which shows the ramp-peak plateau behavior expected in chaotic systems. Then we calculate finite temperature OTOCs and show that scrambling time t_s scales as t_s~log(N) where N is the system size and the Lyapunov exponents extracted from these OTOCs decay as a function of 1/β both of which are characteristics of fast scrambling. Our results indicate that this simple model with only site-dependent couplings can capture intricate dynamics of fast scramblers without the need for all-to-all connections and is an ideal test-bed for future studies of scrambling and quantum chaos on quantum computers due to the modest resources needed to achieve quantum simulations of this model.