gftool.hubbard_dimer_gf_z

gftool.hubbard_dimer_gf_z(z, hopping, interaction, kind='+')

Green’s function for the two site Hubbard model on a dimer.

The Hamilton is given

\[H = -t∑_{σ}(c^†_{1σ} c_{2σ} + c^†_{2σ} c_{1σ}) + U∑_i n_{i↑} n_{i↓}\]

with the hopping \(t\) and the interaction \(U\). The Green’s function is given for the operators \(c_{±σ} = 1/√2 (c_{1σ} ± c_{2σ})\), where \(±\) is given by kind

Parameters:

zcomplex ndarray or complex

Green’s function is evaluated at complex frequency z.

hoppingfloat

The hopping parameter between the sites of the dimer.

interactionfloat

The Hubbard interaction strength for the on-site interaction.

kind{‘+’, ‘-‘}

The operator for which the Green’s function is calculated.

Returns:

complex ndarray

Value of the Hubbard dimer Green’s function at frequencies z.

Notes

The solution is obtained by exact digitalization and shown in [eder2017].

References

[eder2017]

Eder, Robert. “Introduction to the Hubbard Mode.” In The Physics of Correlated Insulators, Metals and Superconductors, edited by Eva Pavarini, Erik Koch, Richard Scalettar, and Richard Martin. Schriften Des Forschungszentrums Jülich Reihe Modeling and Simulation 7. Jülich: Forschungszentrum Jülich, 2017. https://www.cond-mat.de/events/correl17/manuscripts/eder.pdf.