gftool.hubbard_I_self_z

gftool.hubbard_I_self_z(z, U, occ)

Self-energy in Hubbard-I approximation (atomic solution).

The chemical potential and the onsite energy have to be included in z.

Parameters:

zcomplex array_like

The complex frequencies at which the self-energy is evaluated. z should be shifted by the onsite energy and the chemical potential.

Ufloat array_like

The local Hubbard interaction U.

occfloat array_like

The occupation of the opposite spin as the spin of the self-energy.

Returns:

complex array_like

The self-energy in Hubbard I approximation.

Examples

>>> U = 5
>>> mu = U/2  # particle-hole symmetric case -> n=0.5
>>> ww = np.linspace(-5, 5, num=1000) + 1e-6j

>>> self_ww = gt.hubbard_I_self_z(ww+mu, U, occ=0.5)

Show the spectral function for the Bethe lattice, we see the two Hubbard bands centered at ±U/2:

>>> import matplotlib.pyplot as plt
>>> gf_iw = gt.bethe_gf_z(ww+mu-self_ww, half_bandwidth=1.)
>>> __ = plt.plot(ww.real, -1./np.pi*gf_iw.imag)
>>> plt.show()

(png, pdf)