Evolution of Entanglement Entropy in One-Dimensional Systems

Details Evolution of Entanglement Entropy in One-Dimensional Systems Evolution of Entanglement Entropy in One-Dimensional Systems

2005-03-16

arxiv.org/abs/cond-mat/0503393v1

J.Stat.Mech.0504:P04010,2005

Physics

Condensed Matter

Statistical Mechanics

26 pages, 7 figures

Scientific paper

10.1088/1742-5468/2005/04/P04010

We study the unitary time evolution of the entropy of entanglement of a one-dimensional system between the degrees of freedom in an interval of length l and its complement, starting from a pure state which is not an eigenstate of the hamiltonian. We use path integral methods of quantum field theory as well as explicit computations for the transverse Ising spin chain. In both cases, there is a maximum speed v of propagation of signals. In general the entanglement entropy increases linearly with time $t$ up to t=l/2v, after which it saturates at a value proportional to l, the coefficient depending on the initial state. This behavior may be understood as a consequence of causality.

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