Steady state of interacting Floquet insulators

TL;DR

This paper investigates how to achieve and control a non-trivial nonequilibrium steady state in interacting Floquet insulators by coupling to a phonon bath, using Floquet-Boltzmann equations and rate models.

Contribution

It introduces a method to control Floquet eigenstate populations via dissipation and demonstrates the existence of an insulator-like steady state with low excitations.

Findings

Electronic populations can be controlled by dissipation.

Steady state can resemble an insulator with low excitations.

A simple rate equation captures the steady state behavior.

Abstract

Floquet engineering offers tantalizing opportunities for controlling the dynamics of quantum many body systems and realizing new nonequilibrium phases of matter. However, this approach faces a major challenge: generic interacting Floquet systems absorb energy from the drive, leading to uncontrolled heating which washes away the sought after behavior. How to achieve and control a non-trivial nonequilibrium steady state is therefore of crucial importance. In this work, we study the dynamics of an interacting one-dimensional periodically-driven electronic system coupled to a phonon heat bath. Using the Floquet-Boltzmann equation (FBE) we show that the electronic populations of the Floquet eigenstates can be controlled by the dissipation. We find the regime in which the steady state features an insulatorlike filling of the Floquet bands, with a low density of additional excitations. Furthermore, we develop a simple rate equation model for the steady state excitation density that captures the behavior obtained from the numerical solution of the FBE over a wide range of parameters.