Local quantum criticality out of equilibrium - effective temperatures and scaling in the steady state regime

TL;DR

This paper investigates the non-equilibrium steady state properties of a Bose-Fermi-Kondo model, revealing fixed-point-dependent effective temperatures and scaling behaviors in charge and energy currents under bias voltage and temperature gradients.

Contribution

It introduces a dynamical large-N approach to analyze non-equilibrium fixed points and identifies effective temperatures from fluctuation dissipation relations in the model.

Findings

Existence of fixed-point-dependent effective temperatures.

Scaling behavior of charge and energy currents characterized.

Recovery of equilibrium spin susceptibilities using effective temperatures.

Abstract

We study the out of equilibrium steady state properties of the Bose-Fermi-Kondo model, describing a local magnetic moment coupled to two ferromagnetic leads that support bosonic (magnons) and fermionic (Stoner continuum electrons) low energy excitations. This model describes the destruction of the Kondo effect as the coupling to the bosons is increased. Its phase diagram comprises three non-trivial fixed points. Using a dynamical large-$N$approach on the Keldysh contour, we study two different non-equilibrium setups: (a) a finite bias voltage and (b) a finite temperature gradient, imposed across the leads. The scaling behavior of the charge and energy currents is identified and characterized for all fixed points. We report the existence of a fixed-point-dependent effective temperature, defined though the fluctuation dissipation relations of the local spin-susceptibility in the scaling regime, which permits to recover the equilibrium behavior of both dynamical and static spin susceptibilities.