Thermodynamics and Many Body Chaos for generalized large q SYK models

Abstract

This paper considers a type of generalized large $q$ SYK models which include multi-body interactions between Majorana fermions. We derive an effective action in the limit of large $N$ and large $q$ (with $\frac{q^2}{N}$ small), and find a universal expression for thermodynamical quantities. We also consider the chaos exponent using the retarded kernel method and find an efficient way to calculate the Lyapunov exponent for generalized large $q$ SYK models numerically.

20 pages, 4 figures