gftool.lattice.square.stress_trafo
- gftool.lattice.square.stress_trafo(xi, half_bandwidth)[source]
Single pole integration over the stress tensor function.
In analogy to the Hilbert transformation, we define the stress tensor transformation as
\[T(ξ) = ∫dϵ \tilde{Φ}_{xx}(ϵ)/(ξ - ϵ)\]with the stress tensor function
\[\tilde{Φ}_{xx}(ϵ) ≔ ∑_k 𝜕^2/𝜕k_x^2 δ(ϵ - ϵ_k) = -0.5 * ϵ * DOS(ϵ)\]- Parameters:
- xicomplex or complex array_like
Point of evaluation of the transformation.
- half_bandwidthfloat
Half-bandwidth of the square lattice.
- Returns:
- complex np.ndarray
Stress tensor function at xi.
References
[arsenault2013]Arsenault, L.-F., Tremblay, A.-M.S., 2013. Transport functions for hypercubic and Bethe lattices. Phys. Rev. B 88, 205109. https://doi.org/10.1103/PhysRevB.88.205109