Numerical renormalization group study of Loschmidt echo in Kondo system

We analyze time evolution of the Loschmidt echo following a quench in Hamiltonian variables of the Kondo system. Firstly, we study the one-channel Kondo model and find the universal behavior of the Loschmidt echo. Here, the relevant time scale is given by the inverse of the Kondo temperature. For the two-channel model, we focus on the quench leading to the formation of the non-Fermi liquid state and discuss the relevant dynamics. Furthermore, we study the case when the system initially prepared in Fermi liquid phase is suddenly coupled to the second screening channel. A new time scale emerges, which is associated with the channel anisotropy.

Finally, we study the post-quench dynamical behavior of the Kondo system in the presence of external magnetic field. Time dependence of the impurity’s magnetization sheds new light on identification of the relevant time scales in the dynamics.