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

• \(\epsilon_i\), eps1 and eps2, energy levels

• \(U_i\), U1 and U2, 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.