gftool.lattice.sc.dos_mp
- gftool.lattice.sc.dos_mp(eps, half_bandwidth=1)[source]
Multi-precision DOS of non-interacting 3D simple cubic lattice.
Has a van Hove singularity (continuous but not differentiable) at abs(eps) = D/3.
Implements Eq. 7.37 from [joyce1973] for the special case of eps = 0, otherwise calls
gf_z_mp
.- Parameters:
- epsmpmath.mpf or mpf_like
DOS is evaluated at points eps.
- half_bandwidthmpmath.mpf or mpf_like
Half-bandwidth of the DOS of the simple cubic lattice. The half_bandwidth corresponds to the nearest neighbor hopping \(t=D/6\).
- Returns:
- mpmath.mpf
The value of the DOS.
References
[economou2006]Economou, E. N. Green’s Functions in Quantum Physics. Springer, 2006.
[joyce1973]G. S. Joyce, Phil. Trans. of the Royal Society of London A, 273, 583 (1973). https://www.jstor.org/stable/74037
[katsura1971]S. Katsura et al., J. Math. Phys., 12, 895 (1971). https://doi.org/10.1063/1.1665663
Examples
>>> eps = np.linspace(-1.1, 1.1, num=501) >>> dos_mp = [gt.lattice.sc.dos_mp(ee, half_bandwidth=1) for ee in eps] >>> dos_mp = np.array(dos_mp, dtype=np.float64)
>>> import matplotlib.pyplot as plt >>> _ = plt.axvline(1/3, color="black", linewidth=0.8) >>> _ = plt.axvline(-1/3, color="black", linewidth=0.8) >>> _ = plt.plot(eps, dos_mp) >>> _ = plt.xlabel(r"$\epsilon/D$") >>> _ = plt.ylabel(r"DOS * $D$") >>> _ = plt.axvline(0, color="black", linewidth=0.8) >>> _ = plt.ylim(bottom=0) >>> _ = plt.xlim(left=eps.min(), right=eps.max()) >>> plt.show()