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

¹ Max Planck Institute for the Physics of Complex Systems - Nöthnitzer Str. 38, D-01187 Dresden, Germany, EU
² Max Planck Institute for Chemical Physics of Solids - Nöthnitzer Str. 40, D-01187 Dresden, Germany, EU
³ Department of Physics and Astronomy, Rice University - Houston, TX 77005, USA

Received: 14 March 2013
Accepted: 21 May 2013

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.