This is the single-impurity single-orbital Anderson model with conserved total charge (Q) and z-component of total spin (Sz) quantum numbers.


\[H_\mathrm{imp} = \epsilon_1 n + U_1 n_\uparrow n_\downarrow + B_1 S_z\]


\[S_z = \frac{1}{2} \left( n_\uparrow - n_\downarrow \right)\]


  • \(\epsilon_1\), eps1, energy level

  • \(U_1\), U1, electron-electron interaction

  • \(B_1\), B1, magnetic field (Zeeman splitting)

Expectation values

  • \(\langle n \rangle\), n_d, impurity occupancy

  • \(\langle n^2 \rangle\), n_d^2, impurity occupancy squared

  • \(\langle \sum_\sigma d^\dagger_\sigma f_{0\sigma} + \text{h.c.} \rangle\), hop0, hopping between the impurity and the zero-th site of the Wilson chain

  • \(\langle S_z \rangle\), SZd, spin polarization (magnetization)

Structure of Green’s functions

Two blocks, up and dn, scalar-valued (1x1 matrix)

Dynamic susceptibilities

Dynamic spin and charge susceptibilities are calculated.