  We analyze the process of thermalization, dynamics and the eigenstate
thermalization hypothesis (ETH) for the single impurity Anderson model,
focusing on the Kondo regime. For this we construct the complete eigenbasis of
the Hamiltonian using the numerical renormalization group (NRG) method in the
language of the matrix product states. It is a peculiarity of the NRG that
while the Wilson chain is supposed to describe a macroscopic bath, very few
single particle excitations already suffice to essentially thermalize the
impurity system at finite temperature, which amounts to having added a
macroscopic amount of energy. Thus given an initial state of the system such as
the ground state together with microscopic excitations, we calculate the
spectral function of the impurity using the microcanonical and diagonal and
grand canonical ensembles. By adding or removing particles at a certain Wilson
energy shell on top of the ground state, we find qualitative agreement between
the spectral functions calculated for different ensembles. This indicates that
the system thermalizes in the long-time limit, and can be described by an
appropriate statistical-mechanical ensemble. Moreover, by calculating the
impurity spectral density at the Fermi level and the dot occupancy for energy
eigenstates relevant for microcanonical ensemble, we find good support for ETH.
The ultimate mechanism responsible for this effective thermalization within the
NRG can be identified as Anderson orthogonality: the more charge that needs to
flow to or from infinity after applying a local excitation within the Wilson
chain, the more the system looks thermal afterwards at an increased
temperature. For the same reason, however, thermalization fails if charge
rearrangement after the excitation remains mostly local.
