gftool.lattice.square.stress_trafo

gftool.lattice.square.stress_trafo(xi, half_bandwidth)

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.

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