Bounding entanglement spreading after a local quench
Abstract
We consider the variation of von Neumann entropy of subsystem reduced states of general manybody lattice spin systems due to local quantum quenches. We obtain LiebRobinsonlike bounds that are independent of the subsystem volume. The main assumptions are that the Hamiltonian satisfies a LiebRobinson bound and that the volume of spheres on the lattice grows at most exponentially with their radius. More specifically, the bound exponentially increases with time but exponentially decreases with the distance between the subsystem and the region where the quench takes place. The fact that the bound is independent of the subsystem volume leads to stronger constraints (than previously known) on the propagation of information throughout manybody systems. In particular, it shows that bipartite entanglement satisfies an effective "light cone," regardless of system size. Further implications to t densitymatrix renormalizationgroup simulations of quantum spin chains and limitations to the propagation of information are discussed.
 Publication:

Physical Review A
 Pub Date:
 June 2017
 DOI:
 10.1103/PhysRevA.95.062301
 arXiv:
 arXiv:1706.01917
 Bibcode:
 2017PhRvA..95f2301D
 Keywords:

 Quantum Physics
 EPrint:
 12 pages, 1 figure