Nonequilibrium occupation number and charge susceptibility of a resonance level close to a dissipative quantum phase transition

Abstract

Based on the recent paper [Phys. Rev. Lett. 102, 216803 (2009)], we study the nonequilibrium occupation number n(d) and charge susceptibility chi of a resonance level close to dissipative quantum phase transition of the Kosterlitz-Thouless (KT) type between a delocalized phase for weak dissipation and a localized phase for strong dissipation. The resonance level is coupled to two spinless fermionic baths with a finite bias voltage and an Ohmic bosonic bath representing the dissipative environment. The system is equivalent to an effective anisotropic Kondo model out of equilibrium. Within the nonequilibrium renormalization-group approach, we calculate nonequilibrium magnetization M and spin susceptibility chi in the effective Kondo model, corresponding to 2n(d)-1 and chi of a resonance level, respectively. We demonstrate the smearing of the KT transition in the nonequilibrium magnetization M as a function of the effective anisotropic Kondo couplings, in contrast to a perfect jump in M at the transition in equilibrium. In the limit of large bias voltages, we find M and chi at the KT transition and in the localized phase show deviations from the equilibrium Curie-law behavior. As the system gets deeper in the localized phase, both n(d)-1/2 and chi decrease more rapidly to zero with increasing bias voltages.