Short-time versus long-time dynamics of entanglement in quantum lattice models

R. G. Unanyan, D. Muth, M. Fleischhauer
2010 Physical Review A. Atomic, Molecular, and Optical Physics  
We study the short-time evolution of the bipartite entanglement in quantum lattice systems with local interactions in terms of the purity of the reduced density matrix. A lower bound for the purity is derived in terms of the eigenvalue spread of the interaction Hamiltonian between the partitions. Starting from an initially separable state the purity decreases as 1 - (t/τ)^2, i.e. quadratically in time, with a characteristic time scale τ that is inversly proportional to the boundary size of the
more » ... ubsystem, i.e., as an area-law. For larger times an exponential lower bound is derived corresponding to the well-known linear-in-time bound of the entanglement entropy. The validity of the derived lower bound is illustrated by comparison to the exact dynamics of a 1D spin lattice system as well as a pair of coupled spin ladders obtained from numerical simulations.
doi:10.1103/physreva.81.022119 fatcat:uuy5aplrjfeologt5g2uvauasm