  Using the natural orbitals renormalization group (NORG) method, we have
investigated the screening of the local spin of an Anderson impurity
interacting with the helical edge states in a quantum spin Hall insulator. We
find that there is a local spin formed at the impurity site and the local spin
is completely screened by electrons in the quantum spin Hall insulator.
Meanwhile, the local spin is screened dominantly by a single active natural
orbital. We then show that the Kondo screening mechanism becomes transparent
and simple in the framework of natural orbitals formalism. We project the
active natural orbital respectively into real space and momentum space to
characterize its structure. And we confirm the spin-momentum locking property
of the edge states based on the occupancy of a Bloch state in the edge to which
the impurity couples. Furthermore, we study the dynamical property of the
active natural orbital represented by the local density of states, from which
we observe the Kondo resonance peak.
