gftools

Collection of commonly used Green’s functions and utilities.

Main purpose is to have a tested base.

Submodules

• gftools.fourier
• gftools.lattice
• gftools.matrix
• gftools.pade

Glossary

DOS

Density of States

eps

<ϵ, epsilon> (real) energy variable. Typically used for for the DOS where it replaces the k-dependent Dispersion \(ϵ_k\).

iv

Bosonic Matsubara frequncies

iw

<iω_n> Fermionic Matusbara frequncies

tau

Imaginary time points

z

Complex frequency variable

API

Functions

check_convergence(gf_iw, potential, beta[, …])	Return data for visual inspection of the density error.
density(gf_iw, potential, beta[, …])	Calculate the number density of the Green’s function gf_iw at finite temperature beta.
density_error(delta_gf_iw, iw_n[, noisy])	Return an estimate for the upper bound of the error in the density.
fermi_fct(eps, beta)	Return the Fermi function 1/(exp(βϵ)+1).
fermi_fct_d1(eps, beta)	Return the 1st derivative of the Fermi function.
fermi_fct_inv(fermi, beta)	Inverse of the Fermi function.
hubbard_I_self_z(z, U, occ)	Self-energy in Hubbard-I approximation (atomic solution).
hubbard_dimer_gf_z(z, hopping, interaction)	Green’s function for the two site Hubbard model on a dimer.
matsubara_frequencies(n_points, beta)	Return fermionic Matsubara frequencies \(iω_n\) for the points n_points.
matsubara_frequencies_b(n_points, beta)	Return bosonic Matsubara frequencies \(iν_n\) for the points n_points.
pole_gf_tau(tau, poles, weights, beta)	Imaginary time Green’s function given by a finite number of poles.
pole_gf_z(z, poles, weights)	Green’s function given by a finite number of poles.
surface_gf_zeps(z, eps, hopping_nn)	Surface Green’s function for stacked layers.

Classes

Result(x, err)