Numerical renormalization group study of the Loschmidt echo in Kondo systems

Abstract

AbstractWe study the dynamical properties of the one-channel and two-channel spin-1/2 Kondo models after quenching in Hamiltonian variables. Eigen spectrum of the initial and final Hamiltonians is calculated by using the numerical renormalization group method implemented within the matrix product states formalism. We consider multiple quench protocols in the considered Kondo systems, also in the presence of external magnetic field of different intensities. The main emphasis is put on the analysis of the behavior of the Loschmidt echo L(t), which measures the ability of the system’s revival to its initial state after a quench. We show that the decay of the Loschmidt echo strongly depends on the type of quench and the ground state of the system. For the one-channel Kondo model, we show that L(t) decays as, $$L(t)\sim (t\cdot T_K)^{-1.4}$$ L ( t ) ∼ ( t · T K ) - 1.4 , where $$T_K$$ T K is the Kondo temperature, while for the two-channel Kondo model, we demonstrate that the decay is slower and given by $$L(t)\sim (t\cdot T_K)^{-0.7}$$ L ( t ) ∼ ( t · T K ) - 0.7 . In addition, we also determine the dynamical behavior of the impurity’s magnetization, which sheds light on identification of the relevant time scales in the system’s dynamics.