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We study the short-time evolution of the bipartite entanglement in quantumlattice systems with local interactions in terms of the purity of the reduceddensity matrix. A lower bound for the purity is derived in terms of theeigenvalue spread of the interaction Hamiltonian between the partitions.Starting from an initially separable state the purity decreases as $1 -(t/\tau)^2$, i.e. quadratically in time, with a characteristic time scale$\tau$ that is inversly proportional to the boundary size of the subsystem,i.e., as an area-law. For larger times an exponential lower bound is derivedcorresponding to the well-known linear-in-time bound of the entanglemententropy. The validity of the derived lower bound is illustrated by comparisonto the exact dynamics of a 1D spin lattice system as well as a pair of coupledspin ladders obtained from numerical simulations.

Short-time vs. long-time dynamics of entanglement in quantum lattice models