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We study the Ising spin chain with a Dzyaloshinskii-Moriya interactionfocusing on the static and dynamic properties of the entanglement entropy,following a quantum quench. We show that the effects of the additionalanisotropic interaction on the phase diagram and on the dynamics of the systemare captured by the properties of the entanglement entropy. In particular, themodel provides a way to study the quench dynamics in a system with an energycurrent. We consider quenches starting from an initial excited state of theIsing spin chain, and we analyze the effects of different initial conditions.

Entanglement and its evolution after a quench in the presence of an energy current