Dynamic renormalization group theory for open Floquet systems

TL;DR

This paper develops a dynamic renormalization group approach for open Floquet systems, revealing how periodic driving inhibits critical fluctuations and scale invariance near phase transitions.

Contribution

It introduces a perturbative RG framework combining Keldysh and Floquet formalisms, accounting for dynamic sectors and finite drive frequencies in open driven systems.

Findings

Periodic drive inhibits critical fluctuations in open Floquet systems

Criticality is only achieved in the zero-frequency limit

Finite drive frequency introduces a scale preventing scale invariance

Abstract

We develop a comprehensive Renormalization Group (RG) approach to criticality in open Floquet systems, where dissipation enables the system to reach a well-defined Floquet steady state of finite entropy, and all observables are synchronized with the drive. We provide a detailed description of how to combine Keldysh and Floquet formalisms to account for the critical fluctuations in the weakly and rapidly driven regime. A key insight is that a reduction to the time-averaged, static sector, is not possible close to the critical point. This guides the design of a perturbative dynamic RG approach, which treats the time-dependent, dynamic sector associated to higher harmonics of the drive, on an equal footing with the time-averaged sector. Within this framework, we develop a weak drive expansion scheme, which enables to systematically truncate the RG flow equations in powers of the inverse drive frequency $\Omega^{-1}$. This allows us to show how a periodic drive inhibits scale invariance and critical fluctuations of second order phase transitions in rapidly driven open systems: Although criticality emerges in the limit $\Omega^{-1}=0$, any finite drive frequency produces a scale that remains finite all through the phase transition. This is a universal mechanism that relies on the competition of the critical fluctuations within the static and dynamic sectors of the problem.