The p-spin Glass Model: A Holographer's Perspective
I will discuss a large-N bosonic quantum mechanical sigma-model with a spherical target space subject to disordered interactions, more colloquially known as the p-spin spherical model. Replica symmetry is broken at low temperatures and for sufficiently weak quantum fluctuations, which drives the system into a spin glass phase. This spin glass phase exhibits an emergent conformal symmetry in the strong coupling regime, which dictates its thermodynamic properties. I will discuss an approximate analytical solution to the spin glass equations, which interpolates between the conformal regime and a finite short-distance solution. I will also discuss the real-time dynamics of the model with emphasis on quantum chaos as measured by out-of-time-order four-point functions. We find exponential Lyapunov growth, which intricately depends on the model's couplings. The spin glass phase also exhibits quantum chaos, albeit with parametrically smaller Lyapunov exponent than in the replica symmetric phase. An analytical calculation in the spin glass phase suggests that this Lyapunov exponent vanishes in a particular infinite coupling limit. I will comment on the potential meaning of these observations from the perspective of holography.