energy orbitals are certainly entangled with the impurity spin. In Fig. 5(b), we show the size dependence of the ↑ - electron density at j = N/ 2 + 1 for N = 6, 8, 10 and 12. We can easily see that, as J$_{K}$ increases, ρ ( N ) N +1 / 2 , ↑ approaches ρ ≃ 0 . 5; the S z = 1 / 2 at the impurity is passed on the orbitals at the lowest energy scale around the Fermi surface, and the number of the orbital sites is effectively reduced to be N − 1. Moreover, as N in- creases with J$_{K}$ fixed, ρ ( N ) N +1 / 2 , ↑ approaches the value of the strong coupling limit. This behavior is of course equivalent to the iterative process of the Wilson NRG. On the other hand, the ↑ -electron density in the highest energy scale ρ ( N ) N ↑ shows little size dependence, which is almost negligible within the scale of Fig.5(b). In Fig. 6, we show the real-space distribution of the spin density of the groundstate for N = 14. Note that the charge distribution of all J$_{K}$ is uniform in the real space, indicating the spin-charge separation. The singlet pair of the impurity and the orbital electron itself is in- visible to a spin expectation value. However, one can extract an essential information from the distribution of magnetization passed on the orbital electrons from the impurity site. We first discuss the strong coupling case J$_{K}$ = 3 . 0. We have confirmed that the spin distribution for J$_{K}$ = 3 . 0 is basically identical to that of J$_{K}$ = 100. The dominant single-particle component in the ground- state is the orbitals around the Fermi surface( j = 7 and 8 for N = 14). On the other hand, the groundstate wave- function also includes certain amplitudes of the higher energy orbitals, as can be seen in Figs. 5. The decay rate of the spin density in the strong coupling limit is expected to be close to the canonical value λ = ln 2 / 2 ≃ 3 . 47, but to have a certain deviation from it. In Fig. 6, the open circle at n =even is very similar to the dotted line of the free orbital of j = 8, but a precise analysis for the decay rate of the spin density for J$_{K}$ = 3 . 0 at n =even sites actually gives λ ∗ = 0 . 312 ≃ 0 . 9 λ . In addition, we can see that the spin density at n =odd sites clearly deviates from the single particle result. The above results of the S z distribution illustrate that the wavefunction in the strong-coupling limit includes the nontrivial correlation effect, where λ is slightly renormalized to λ ∗ ≃ 0 . 9 λ . This suggests that the scale factor could be also renormalized to e 2 λ $^{∗}$M from the canonical value in the wavefunction level. We next turn to the case of J$_{K}$ = 0 . 5, which is in the crossover regime of the Kondo coupling within N = 14. For J$_{K}$ = 0 . 5, the total- S z of the orbital electron is 0 . 233, which implies that the screening rate of the impurity spin is 47%. Then, we can see that the decay rate reduces to be λ ∗ = 0 . 215 ≃ 0 . 62 λ , which illustrates that the wave- function in the crossover regime is entangled with the states in the wide range of the energy scale. In the con- text of the wavepacket basis, this implies that hybridiza- tion of the higher-energy orbitals generates an eigenvalue of the lower-energy scale. As the system size N increases, FIG. 6: (Color online)Spin distribution in the real-space rep- resentation for N = 14 and λ = ln 2 / 2. The open(solid) circle indicates J$_{K}$ = 3 . 0(0.5). n denotes the lattice index, where n = 14 corresponds to the impurity site. The dotted line means the spin distribution of the free orbital of j = 8. FIG. 5: (Color online) (a) Kondo coupling dependences of ↑ - electron density for N = 12 with λ = ln 2 / 2 ≃ 0 . 347(Λ = √$_{2),}$ where j denotes the index of the orbitals. The Fermi surface of the free orbital electron corresponds to j = 6 . 5. (b) Size dependences of ↑ -electron density for λ ≃ 0 . 347(Λ = √$_{2).}$ $^{The curves indicate the}$↑-electron density at the Fermi surface ρ ( N ) N/ 2+1 ↑ for N = 6, 8, 10, and 12 from down to up. The solid curves of ρ ( N ) N ↑ represent the ↑ -electron density at the highest energy scale orbital. 6 0 10 10 −4 10 −2 n S z n J$_{K}$ =0.5 J$_{K}$ =3.0  0  0.5  1  1.5  2  2.5  3  0  2  4  6  8  10  12  0  0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  1 j J$_{K}$ j  0 1 2 3 0.5 J$_{K}$ N N N N/2+1