Given a general many-body quantum system, how can we diagnose whether a holographic causal structure emerges as its number of degrees of freedom goes to infinity? In this talk, I will explain which general tools the language of von Neumann algebras provides us with to address this question. In particular, I will show that a sharp horizon structure emerges in the dual of N=4 SYM theory at finite 't Hooft coupling, which allows to make sense of causality at nonzero string length in string theory. I will also elaborate on an intriguing interplay between the algebraic results we will encounter and the theory of chaos in classical and quantum dynamical systems.