Exercise N4

SU($N)$ Anderson impurity model in the limit of infinite Coulomb interaction ($U = \infty$) at the impurity site.

Consider the Hamiltonian:

$$\begin{array}{l} H = H_{b} + H_{f} + H_{I} \\ H_{b} = {\s... ...g } X_{0m} + V_{k}^{\ast} X_{m0}c_{km}^{} \\ \\ \end{array}$$

Compute the first three moments of $\langle \langle f_{} (\omega )f_{}^{\dag } (\omega )\rangle \rangle$

Namely

$$\begin{array}{l} \langle {\left\{ {X_{n0} X_{0n}} \right\}}... ...ft\{ {[H,X_{n0} ][H,X_{0n} ]} \right\}}\rangle \\ \end{array}$$

What is their physical meaning?