A perturbative renormalization group approach to driven quantum systems

TL;DR

This paper develops a perturbative renormalization group method to analyze driven quantum systems at zero temperature, revealing how drive frequency influences system behavior and criticality.

Contribution

It introduces a novel RG approach for driven quantum systems using a Keldysh diagrammatic technique, linking drive frequency scaling to thermal behavior and identifying conditions for non-Gaussian regimes.

Findings

Drive frequency acts as a cutoff scale in RG flow.

Analytical condition for transition to non-Gaussian regime.

Non-perturbative mode coupling appears at critical points.

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 $\phi^4$ 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.