Characteristic length scales from entanglement dynamics in electric-field-driven tight-binding chains

We study entanglement dynamics in the nearest-neighbor fermionic chain that is subjected to both dc and ac electric fields. The dynamics gives the well-known Bloch oscillations in the dc field case provided that the system size is larger than the Bloch length, whereas in the ac field case the entropy is bounded and oscillates with the driving frequency at the points of dynamic localization, and has a logarithmic growth at other points. A combined ac+dc field yields super-Bloch oscillations for system sizes larger than the super-Bloch length, which puts a constraint on the device size in a typical nonequilibrium setup to observe super-Bloch oscillations where the device is connected to the leads. Entanglement entropy provides useful signatures for all of these phenomena, and an alternate way to capture the various length scales involved.