"This toy model is also a condensed matter system in which the pattern of interaction itself is a quantum degree of freedom instead of being a fixed graph. It can be regarded as a Hubbard model where the strength of the hopping emerges as the mean field value for other quantum degrees of freedom. We show a numerical simulation of the quantum system and results on the asymptotic behavior of the classical system. The numerical simulation is mainly concerned with the entanglement dynamics of the system and the issue of its thermalization as a closed system. A closed system can thermalize in the sense that the partial system shows some typicality, or some relevant observables reach a steady or almost steady value for long times. The issue of thermalization for closed quantum system and the foundations of quantum statistical mechanics gained recently novel interest with the understanding that the role of entanglement plays in it . The behavior of out of equilibrium quantum system under sudden quench, and the approach to equilibrium has been recently the object of study to gain insight in novel and exotic quantum phases like topologically ordered states."