Entanglement in disordered and non-equilibrium systems

We calculate an entanglement witness for a disordered spin system using the method of functional many-body perturbation theory, comparing the effect of taking a quenched and an annealed average over the disorder. We find, on considering the example of an XX Heisenberg spin chain with a Dzyaloshinskii-Moriya interaction, that disorder in the Dzyaloshinskii-Moriya interaction increases the region of entanglement detected by the witness. We also discuss a method of detecting entanglement in far from equilibrium systems.