Based on the recent paper, we study the nonequilibrium occupation number nd and charge susceptibility χ 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 χ in the effective Kondo model, corresponding to 2 nd -1 and χ 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 χ 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 nd -1/2 and χ decrease more rapidly to zero with increasing bias voltages.
|Journal||Physical Review B - Condensed Matter and Materials Physics|
|State||Published - 30 Aug 2010|