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

TL;DR

This paper investigates entanglement dynamics in a fermionic chain under electric fields, revealing how different field conditions affect entropy oscillations, localization, and characteristic length scales, with implications for device size constraints.

Contribution

It introduces a detailed analysis of entanglement entropy as a signature of Bloch and super Bloch oscillations, highlighting the role of characteristic length scales in non-equilibrium quantum systems.

Findings

Entanglement entropy oscillates with the driving frequency during dynamical localization.

System size constraints are identified for observing super Bloch oscillations.

Entanglement provides signatures of various length scales in electric-field-driven chains.

Abstract

We study entanglement dynamics in the nearest-neighbour 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 dynamical localization, and has a logarithmic growth at other points. A combined AC + DC field yields super Bloch oscillations for the system size larger than the super Bloch length which puts a constraint on the device size in a typical non-equilibrium set-up 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.