Entanglement Entropy dynamics in Heisenberg chains

By means of the time-dependent density matrix renormalization groupalgorithm we study the zero-temperature dynamics of the Von Neumannentropy of a block of spins in a Heisenberg chain after a sudden quenchin the anisotropy parameter. In the absence of any disorder the blockentropy increases linearly with time and then saturates.

We analyze thevelocity of propagation of the entanglement as a function of the initialand final anisotropies and compare, wherever possible, our results withthose obtained by means of Conformal Field Theory. In the disorderedcase we find a slower (logarithmic) evolution which may signals theonset of entanglement localization.