Numerical analysis of the spatial range of the Kondo effect

Physical Review B - Condensed Matter and Materials Physics

Volumn 81, Issue 4, 2010, Pages

  Busser C A ^a   Martins, G B ^a   Costa Ribeiro, L ^b,c   Vernek, E ^d   Anda, E V ^b   Dagotto, E ^e,f  

^a OAKLAND UNIVERSITY   (United States)

^b PONTIFICAL CATHOLIC UNIVERSITY OF RIO DE JANEIRO   (Brazil)

^c CENTRO FEDERAL DE EDUCAÇÃO TECNOLÓGICA CELSO SUCKOW DA FONSECA   (Brazil)

^d FEDERAL UNIVERSITY OF UBERLÂNDIA   (Brazil)

^e OAK RIDGE NATIONAL LABORATORY   (United States)

^f UNIVERSITY OF TENNESSEE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77954828573     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.81.045111     Document Type: Article

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37. It is important to comment that, the same analytic calculation performed in Ref., which led to the functional forms used to fit the weak- and strong-coupling numerical data in their Fig., can also be done here (although it is certainly a more involved derivation). However, the authors decided not to do so, in order to shorten the Appendix. This will be done in a forthcoming work.
38. Note that A 0 was not calculated as | F (0) | but through the fittings discussed in Figs.. Therefore, its value and its dependency with Δ, as seen in Fig., do not represent the value or the variation in the area of the Kondo peak.
39. A second extrapolation method can also be used (although not as accurate as the one described in Sec.): one can extrapolate the value of | F (N) | to the thermodynamical limit (1 / L → 0) for each value of N, and then obtain R K by fitting the extrapolated | F (N) | to Eq.. Although there is good qualitative agreement on the values obtained for R K between the two extrapolation methods, we favor the first one, as it involves much less computational effort and is therefore more accurate.
40. The limit in which | F (N) | → 0 determines the order of magnitude of the Kondo cloud. However, the actual values and functional variation in both A 0 and R K in Eq. clearly indicate that R K has a leading contribution in determining the size of the Kondo cloud, given the small variation in A 0 in the region of parameter space associated to the Kondo effect (compare the scales of the vertical axis in Figs.).
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44. Note that, in the dashed (blue) curve, the site to site oscillations [similar to the ones displayed in the inset of Fig.] were removed, to improve clarity and emphasize the oscillating behavior of | F (N) |.