Abstract. We provide a simple proof of the Lieb-Robinson bound and use it to prove the existence of the dynamics for interactions with polynomial decay. We then use our results to demonstrate that there is an upper bound on the rate at which correlations between observables with separated support can accumulate as a consequence of the dynamics.

We investigate the nonequilibrium properties of the transverse XX chain. The steady state can be interpreted as the equilibrium state or the ground state of the effective Hamiltonian, which depends on the initial state. We also study the physical properties of the state at various temperatures, in particular, the effects of quantum phase transition.

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