SIAM (QS)
This is the simplest single-impurity single-orbital Anderson model with conserved total charge (Q) and total spin (S) quantum numbers.
Hamiltonian
\[H_\mathrm{imp} = \epsilon_1 n + U_1 n_\uparrow n_\downarrow\]
where \(n_\sigma = d^\dagger_{\sigma} d_{\sigma}\) and \(n=\sum_\sigma n_\sigma\) with \(\sigma=\uparrow,\downarrow\).
Parameters
- \(\epsilon_1\),
eps1, energy level - \(U_1\),
U1, electron-electron interaction
The number 1 is an orbital index. The choice of including an index (which is not strictly needed here) is to ease writing generic codes that support an arbitrary orbital degeneracy.
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, \(f_0\) (i.e., the local orbital of
the bath at the position of the impurity)
Structure of Green’s functions
Single block imp, scalar-valued (1x1 matrix)
Dynamic susceptibilities
Dynamic spin and charge susceptibilities are calculated.