Numerical renormalization group study of the Loschmidt echo in Kondo systems

Area of Science:

• Condensed Matter Physics
• Quantum Dynamics
• Many-Body Systems

Background:

• The Kondo model describes magnetic impurities in metals, crucial for understanding quantum phenomena.
• Quantum quenches, sudden changes in Hamiltonian parameters, drive systems out of equilibrium, revealing novel dynamics.
• Loschmidt echo quantifies quantum state survival after a perturbation, offering insights into system stability.

Purpose of the Study:

• To explore the dynamical properties of one-channel and two-channel spin-1/2 Kondo models after Hamiltonian quenches.
• To analyze the behavior of the Loschmidt echo and impurity magnetization to understand system revival and time scales.
• To investigate the impact of different quench protocols and external magnetic fields on Kondo model dynamics.

Main Methods:

• Numerical Renormalization Group (NRG) method for calculating eigen spectra.
• Matrix Product States (MPS) formalism for efficient numerical implementation.
• Analysis of Loschmidt echo decay L(t) and impurity magnetization dynamics.

Main Results:

• Loschmidt echo decay rates were determined for both one-channel and two-channel Kondo models.
• A distinct decay behavior was observed: L(t) ~ (T_K/t)^2 for the one-channel model and L(t) ~ (T_K/t)^4 for the two-channel model.
• Dynamical behavior of impurity magnetization was calculated, identifying key time scales.

Conclusions:

• The decay of the Loschmidt echo is strongly dependent on the Kondo model type (one-channel vs. two-channel) and the system's ground state.
• The two-channel Kondo model exhibits slower Loschmidt echo decay compared to the one-channel model.
• The study provides insights into the non-equilibrium dynamics and characteristic time scales of quenched Kondo systems.