Quantum many-body dynamics on the star graph

We study 2-local Hamiltonian quantum systems, consisting of qubits interacting on the star graph of N vertices. We numerically demonstrate that these models are generically non-integrable at infinite temperature, and find evidence for a finite temperature phase transition to a glassy phase in generic models. Operators can become complicated in constant time: we explicitly find that there is no bound on out-of-time-ordered correlators, even at finite temperature. Operator growth is not correctly modeled by stochastic quantum dynamics, including Brownian Hamiltonian dynamics or random unitary circuits. The star graph (and similar constructions) may serve as a useful testing ground for conjectures about universality, quantum chaos and Planckian dissipation in k-local systems, including in experimental quantum simulators.