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

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

2009-10-20

arxiv.org/abs/0910.3868v3

Phys. Rev. A 81, 022119 (2010)

Physics

Quantum Physics

some minor additions, 6 pages, 3 figures

Scientific paper

10.1103/PhysRevA.81.022119

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 $1 - (t/\tau)^2$, 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 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.

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