2orb-UJ (QS)
This is the two-orbital Anderson impurity model with conserved total charge (Q) and total spin (S) quantum numbers.
Hamiltonian
\[H_\mathrm{imp} = \sum_{i} \epsilon_i n_i + \sum_i U_i n_{i,\uparrow} n_{i,\downarrow} + U_{12} n_1 n_2 + J_{12} \mathbf{S}_1 \cdot \mathbf{S}_2\]
where \(\mathbf{S}_i\) are the spin operators:
\[\mathbf{S}_i = \frac{1}{2} d_{i\alpha}^\dagger \boldsymbol{\sigma}_{\alpha\beta} d_{i\beta}\]
Parameters
- \(\epsilon_i\),
eps1andeps2, energy levels - \(U_i\),
U1andU2, electron-electron interaction - \(U_{12}\),
U12, inter-level charge repulsion - \(J_{12}\),
J12, inter-level exchange (Hund’s) coupling
Expectation values
- \(\langle n_1 \rangle\),
n_d1, orbital 1 impurity occupancy - \(\langle n_1^2 \rangle\),
n_d1^2, orbital 1 impurity occupancy squared - \(\langle n_2 \rangle\),
n_d2, orbital 2 impurity occupancy - \(\langle n_2^2 \rangle\),
n_d2^2, orbital 2 impurity occupancy squared - \(\langle n_1 n_2 \rangle\),
n_d1n_d2, charge correlation - \(\langle \mathbf{S}_1 \cdot \mathbf{S}_2 \rangle\),
S_d1S_d2, spin correlation
Structure of Green’s functions
Single block imp, 2x2 matrix-valued
Dynamic susceptibilities
Dynamic spin and charge susceptibilities are calculated.