gftool.bcc_gf_z¶
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gftool.bcc_gf_z(z, half_bandwidth)¶ Local Green’s function of 3D body-centered cubic (bcc) lattice.
Has a van Hove singularity at z=0 (divergence).
Implements equations (2.1) and (2.4) from [morita1971]
- Parameters
- zcomplex np.ndarray or complex
Green’s function is evaluated at complex frequency z.
- half_bandwidthfloat
Half-bandwidth of the DOS of the body-centered cubic lattice. The half_bandwidth corresponds to the nearest neighbor hopping t=D/8
- Returns
- gf_zcomplex np.ndarray or complex
Value of the body-centered cubic Green’s function at complex energy z.
References
- morita1971
Morita, T., Horiguchi, T., 1971. Calculation of the Lattice Green’s Function for the bcc, fcc, and Rectangular Lattices. Journal of Mathematical Physics 12, 986–992. https://doi.org/10.1063/1.1665693
Examples
>>> ww = np.linspace(-1.5, 1.5, num=500) >>> gf_ww = gt.lattice.bcc.gf_z(ww, half_bandwidth=1)
>>> import matplotlib.pyplot as plt >>> _ = plt.axhline(0, color='black', linewidth=0.8) >>> _ = 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.xlim(left=ww.min(), right=ww.max()) >>> _ = plt.legend() >>> plt.show()
