Nonlinear current response of an isolated system of interacting fermions

TL;DR

This paper investigates the nonlinear current response of a one-dimensional system of interacting spinless fermions, revealing how nonlinearity can often be incorporated into linear response theory through energy renormalization, with distinct behaviors in integrable versus non-integrable cases.

Contribution

It demonstrates that for non-integrable systems at finite temperatures, nonlinear effects can be effectively captured by linear response with energy renormalization, and characterizes the distinct oscillatory behavior in integrable systems.

Findings

Non-integrable systems' nonlinearity can be approximated by linear response with Joule heating renormalization.

Integrable systems exhibit damped oscillating currents with frequencies related to Bloch oscillations.

The study distinguishes universal behaviors between integrable and non-integrable regimes.

Abstract

Nonlinear real-time response of interacting particles is studied on the example of a one-dimensional tight-binding model of spinless fermions driven by electric field. Using equations of motion and numerical methods we show that for a non-integrable case at finite temperatures the major effect of nonlinearity can be taken into account within the linear response formalism extended by a renormalization of the kinetic energy due to the Joule heating. On the other hand, integrable systems show on constant driving a different universality with a damped oscillating current whereby the frequency is related but not equal to the Bloch oscillations.