Random Matrix Impurity Model

The previous chapter was devoted to the full many-body description of correlations in a disordered host surrounding an impurity. The correlation properties, that can be quantified through the given Kondo temperature, revealed to be mostly related to local quantities, especially the occupation of the impurity level. This can be understood because the non-triviality of the problem comes from the dynamic of the d-level, which becomes frozen if the impurity is fully occupied or empty. To understand the bimodality of the distribution of \(T^{}_{\textrm{K}}\) induced by the plateau in \(P(n^{}_{d})\) around \(n^{}_{d}=1/2\) in the IRLM, the free problem \(U=0\) is further investigated in this chapter. The importance of local properties suggests that the microscopic details of the disordered environment may not be crucial, and that underlying mechanisms could be qualitatively explained by a simpler model, into which the bath part is defined randomly. Numerical and analytical results are both presented in this chapter, and connections with the microscopic model presented in the previous chapter appear through the distribution function \(P(n^{}_{d})\) .