A perturbative renormalization group approach to driven quantum systems

Abstract

We use a perturbative momentum shell renormalization group (RG) approach to study the properties of a driven quantum system at zero temperature. To illustrate the technique, we consider a bosonic ${\varphi }^4$ theory with an arbitrary time dependent interaction parameter $\lambda (t)=\lambda f({\omega }_{0}t)$, where ${\omega }_0$ is the drive frequency and derive the RG equations for the system using a Keldysh diagrammatic technique. We show that the scaling of ${\omega }_0$ is analogous to that of temperature for a system in thermal equilibrium and its presence provides a cutoff scale for the RG flow. We analyze the resultant RG equations, derive an analytical condition for such a drive to take the system out of the gaussian regime, and show that the onset of the non-gaussian regime occurs concomitantly with appearance of non-perturbative mode coupling terms in the effective action of the system. We supplement the above-mentioned results by obtaining them from equations of motions of the bosons and discuss their significance for systems near critical points described by time-dependent Landau-Ginzburg theories.

v2 11pages 7 figs; minor changes from v1

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Cited by in corpus (18)

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• Quantum correlations and entanglement in far-from-equilibrium spin systems
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• Universality in fast quantum quenches
• Universality in driven open quantum matter
• Quantum dynamical field theory for non-equilibrium phase transitions in driven open systems
• Transverse collisional instabilities of a Bose-Einstein condensate in a driven one-dimensional lattice
• Low-frequency phase diagram of irradiated graphene and periodically driven spin-1/2 $XY$ chain
• Renyi entanglement entropy of Fermi liquids and non-Fermi liquids: Sachdev-Ye-Kitaev model and dynamical mean field theories
• Non-Equilibrium Field Theory for Dynamics Starting from Arbitrary Athermal Initial Conditions
• Activating critical exponent spectra with a slow drive
• Phase boundaries in alternating field quantum XY model with Dzyaloshinskii-Moriya interaction: Sustainable entanglement in dynamics
• Tuning towards dynamic freezing using a two-rate protocol
• Absence of Criticality in the Phase Transitions of Open Floquet Systems
• Dynamic renormalization group theory for open Floquet systems
• Fast Scrambling under an RG-flow