gftool.sc_gf_z¶
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gftool.sc_gf_z(z, half_bandwidth=1)¶ Local Green’s function of 3D simple cubic lattice.
Has a van Hove singularity (continuous but not differentiable) at z = ±D/3.
Implements equations (1.24 - 1.26) from [delves2001].
- Parameters
- zcomplex np.ndarray or complex
Green’s function is evaluated at complex frequency z.
- half_bandwidthfloat
Half-bandwidth of the DOS of the simple cubic lattice. The half_bandwidth corresponds to the nearest neighbor hopping \(t=D/6\).
- Returns
- gf_zcomplex np.ndarray or complex
Value of the simple cubic Green’s function at complex energy z.
References
- economou2006
Economou, E. N. Green’s Functions in Quantum Physics. Springer, 2006.
- delves2001
Delves, R. T. and Joyce, G. S., Ann. Phys. 291, 71 (2001). https://doi.org/10.1006/aphy.2001.6148
Examples
>>> ww = np.linspace(-1.1, 1.1, num=500) >>> gf_ww = gt.lattice.sc.gf_z(ww)
>>> import matplotlib.pyplot as plt >>> _ = plt.axhline(0, color="black", linewidth=0.8) >>> _ = plt.axvline(-1/3, color="black", linewidth=0.8) >>> _ = plt.axvline(+1/3, color="black", linewidth=0.8) >>> _ = plt.plot(ww.real, gf_ww.real, label=r"$\Re G$") >>> _ = plt.plot(ww.real, gf_ww.imag, label=r"$\Im G$") >>> _ = plt.ylabel(r"$G*D$") >>> _ = plt.xlabel(r"$\omega/D$") >>> _ = plt.xlim(left=ww.min(), right=ww.max()) >>> _ = plt.legend() >>> plt.show()
