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We demonstrate that the dynamics of an open quantum system can be calculatedefficiently and with predefined error, provided a basis exists in which thesystem-environment interactions are local and hence obey the Lieb-Robinsonbound. We show that this assumption can generally be made. Defining a dynamicalrenormalization group transformation, we obtain an effective Hamiltonian forthe full system plus environment that comprises only those environmentaldegrees of freedom that are within the effective light cone of the system. Thereduced system dynamics can therefore be simulated with a computational effortthat scales at most polynomially in the interaction time and the size of theeffective light cone. Our results hold for generic environments consisting ofeither discrete or continuous degrees of freedom.

Approximating open quantum system dynamics in a controlled and efficient way: A microscopic approach to decoherence