Holstein (QS)
This is the single-orbital Anderson-Holstein model with a single phonon mode.
The phonon cutoff is part of the Hamiltonian specification and it is hard-coded to 10;
the model name is then e.g. Holstein/Nph=10.
Conserved total charge (Q) and total spin (S) quantum numbers.
Hamiltonian
Parameters
\(\epsilon_1\),
eps1, energy level\(U_1\),
U1, electron-electron interaction\(g_1\),
g1, electron-phonon coupling\(n_1\),
n1, offset (charge reference point for e-ph coupling)\(\omega\),
omega, phonon frequency
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\(\langle a^\dagger a \rangle\),
nph, phonon number expectation value\(\langle a+a^\dagger \rangle\),
displ, phonon displacement\(\langle (a+a^\dagger)^2 \rangle\),
displ^2, phonon displacement squared
Structure of Green’s functions
Single block imp, scalar-valued (1x1 matrix)
Dynamic susceptibilities
Dynamic spin and charge susceptibilities are calculated.
Additional quantities
Phonon spectral function.