# Floquet Dynamics of Boundary-Driven Systems at Criticality

## TL;DR

This paper investigates the universal dynamical behavior of boundary-driven quantum critical systems under periodic driving, revealing three distinct regimes and confirming theoretical predictions with numerical simulations.

## Contribution

It introduces a comprehensive analysis of Floquet dynamics at criticality, combining boundary CFT, Kibble-Zurek scaling, and numerical validation to identify universal regimes.

## Key findings

- Identification of three dynamical regimes: slow, fast, and crossover.
- Confirmation of analytic predictions through exact numerics.
- Demonstration of universality in Floquet dynamics with non-integrable perturbations.

## Abstract

A quantum critical system described at low energy by a conformal field theory (CFT) and subjected to a time-periodic boundary drive displays multiple dynamical regimes depending on the drive frequency. We compute the behavior of quantities including the entanglement entropy and Loschmidt echo, confirming analytic predictions from field theory by exact numerics on the transverse field Ising model, and demonstrate universality by adding non-integrable perturbations. The dynamics naturally separate into three regimes: a slow-driving limit, which has an interpretation as multiple quantum quenches with amplitude corrections from CFT; a fast-driving limit, in which the system behaves as though subject to a single quantum quench; and a crossover regime displaying heating. The universal Floquet dynamics in all regimes can be understood using a combination of boundary CFT and Kibble-Zurek scaling arguments.