Dynamic renormalization group theory for open Floquet systems

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.

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Cited by in corpus (5)

• Universality in driven open quantum matter
• Distinctive class of dissipation-induced phase transitions and their universal characteristics
• Mode softening in time-crystalline transitions of open quantum systems
• Analytical Solution for the Steady States of the Driven Hubbard model
• Floquet Renormalization Group Approach to the Periodically Driven Kondo Model