A current algebra approach to the Kondo effect

S. G. Rajeev

Guang-Ming Zhang, Lu Yu

Majorana fermion representations of the algebra associated with spin, charge, and flavour currents have been used to transform the two-channel Kondo Hamiltonian. Using a path integral formulation, we derive a reduced effective action with long-range impurity spin-spin interactions at different imaginary times. In the semiclassical limit, it is equivalent to a one-dimensional Heisenberg spin chain with two-spin, three-spin, etc, long-range interactions, as a generalization of the inverse-square long-range Haldane-Shastry model. In this representation the elementary excitations are `semions', and the non-Fermi liquid low energy properties of the two-channel Kondo model are recovered.

Sergei V. Maleev

Karsten Joho, Stefan Alexander Maier, A. Komnik

We investigate the transient evolution of finite-frequency current noise after the abrupt switching on of the tunneling coupling in two paradigmatic, exactly solvable models of mesoscopic physics: the resonant level model and the Majorana resonant level model, which emerges as an effective model for a Kondo quantum dot at the Toulouse point. We find a parameter window in which the transient noise can become negative, a property it shares with the transient current. However, in contrast to the transient current, which approaches the steady state exponentially fast, we observe an algebraic decay in time of the transient noise for a system at zero temperature. This behavior is dominant for characteristic parameter regimes in both models. At finite temperature the decay is altered from an algebraic to an exponential one with a damping constant proportional to temperature.

Moallison F. Cavalcante, Rodrigo G. Pereira, Maria C. O. Aguiar

We study the real-time dynamics of the Kondo effect after a quantum quench in which a magnetic impurity is coupled to two metallic Hubbard chains. Using an effective field theory approach, we find that for noninteracting electrons the charge current across the impurity is given by a scaling function that involves the Kondo time. In the interacting case, we show that the Kondo time decreases with the strength of the repulsive interaction and the time dependence of the current reveals signatures of the Kondo effect in a Luttinger liquid. In addition, we verify that the relaxation of the impurity magnetization does not exhibit universal scaling behavior in the perturbative regime below the Kondo time. Our results highlight the role of nonequilibrium dynamics as a valuable tool in the study of quantum impurities in interacting systems.