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
\[H_\mathrm{imp} = \epsilon_1 n + U_1 n_\uparrow n_\downarrow + g_1 (a+a^\dagger) (n - n_1) + \omega a^\dagger a\]
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.