  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.
