gftool.lattice.bethez.gf_z

gftool.lattice.bethez.gf_z(z, half_bandwidth, coordination)

Local Green’s function of Bethe lattice for coordination.

\[G(z) = 2 (Z - 1) / z / ((Z - 2) + Z\sqrt{1 - D^2/z^2})\]

where \(D\) is the half_bandwidth and \(Z\) the`coordination`. See [economou2006].

Parameters

zcomplex ndarray or complex

Green’s function is evaluated at complex frequency z

half_bandwidthfloat

Half-bandwidth of the DOS of the Bethe lattice.

coordinationint

Coordination number of the Bethe lattice.

Returns

gf_zcomplex ndarray or complex

Value of the Bethe Green’s function

See also

gftool.lattice.bethe.gf_z

case for coordination=np.infty

gftool.lattice.onedim.gf_z

case for coordination=2

References

economou2006

Economou, E. N. Green’s Functions in Quantum Physics. Springer, 2006.

Examples

>>> ww = np.linspace(-1.5, 1.5, num=500)
>>> gf_ww = gt.lattice.bethez.gf_z(ww, half_bandwidth=1, coordination=9)

>>> import matplotlib.pyplot as plt
>>> _ = plt.plot(ww, gf_ww.real, label=r"$\Re G$")
>>> _ = plt.plot(ww, gf_ww.imag, '--', label=r"$\Im G$")
>>> _ = plt.xlabel(r"$\omega/D$")
>>> _ = plt.ylabel(r"$G*D$")
>>> _ = plt.axhline(0, color='black', linewidth=0.8)
>>> _ = plt.xlim(left=ww.min(), right=ww.max())
>>> _ = plt.legend()
>>> plt.show()

(png, pdf)