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in the spectral density can be restored for both spin orien- tations by properly tuned external magnetic field, which happens for B = B$_{c}$ = 0 . 0020545, where B$_{c}$ (in the units of D) denotes the compensating field. This is in agree- ment with the result obtained earlier. 6,7 Similar behavior also appears for larger positive J , e.g. for J = 0 . 17 shown in Fig. 7(c) and (d). Now, the Kondo resonance becomes restored when the compensating field is B$_{c}$ = 0 . 001928. Note that the magnitude of magnetic field necessary for full restoration of the Kondo effect slightly decreases as J increases. The question which arises now is whether such a restoration by magnetic field is also possible for larger values of J . By fine-tuning in the parameter space of J and B , we have found that this is the case for J below a certain critical value J < ˜ J P c = 0 . 17875. Here ˜ J P c de- notes the critical value of J in the parallel configuration and in the presence of the compensating magnetic field. From numerical results (not shown here), follows that for J > ˜ J P c , the magnetic field can only partially restore the Kondo effect, leading to small side peaks in the spectral function, while the full Kondo peak at ω = 0 cannot be restored. One may now expect that for J = ˜ J P c , the mag- netic field should also restore the quantum critical state. Indeed, by fine-tuning in the parameter space we have found that the quantum critical state can be recovered for B$_{c}$ = 0 . 00191621. This situation is shown explicitly in Fig. 7(e) and (f). Thus, we have shown that in the parallel configuration the properly-tuned magnetic field can restore both the full Kondo effect for J < ˜ J P c as well as the quantum critical state for J = ˜ J P c . 

By comparing numerical curves presented in Fig. 7, one 

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can note that the compensating field B$_{c}$ decreases with increasing the exchange coupling J . This is explicitly shown in Fig. 8, where we have calculated the depen- dence of B$_{c}$ on the exchange coupling J . For J < ˜ J P c , the Kondo resonance can be fully restored by applying compensating field B$_{c}$ . On the other hand, when J > ˜ J P c , the magnetic field cannot compensate the exchange field, so the notion of compensating field becomes meaningless. 

