gftool

Collection of commonly used Green’s functions and utilities.

Main purpose is to have a tested base.

Glossary

DOS
Density of States
eps
epsilon
ϵ
(Real) energy variable. Typically used for for the DOS where it replaces the k-dependent Dispersion \(ϵ_k\).
iv
iν_n
Bosonic Matsubara frequncies
iw
iω_n
Fermionic Matusbara frequncies
tau
τ
Imaginary time points
z
Complex frequency variable

API

Functions

bethe_dos(eps, half_bandwidth) DOS of non-interacting Bethe lattice for infinite coordination number.
bethe_dos_moment(m, half_bandwidth) Calculate the m th moment of the Bethe DOS.
bethe_gf_d1_z(z, half_bandwidth) First derivative of local Green’s function of Bethe lattice for infinite coordination number.
bethe_gf_d2_z(z, half_bandwidth) Second derivative of local Green’s function of Bethe lattice for infinite coordination number.
bethe_gf_z(z, half_bandwidth) Local Green’s function of Bethe lattice for infinite coordination number.
bethe_hilbert_transform(xi, half_bandwidth) Hilbert transform of non-interacting DOS of the Bethe lattice.
bose_fct(eps, beta) Return the Bose function 1/(exp(βϵ)-1).
check_convergence(gf_iw, potential, beta[, …]) Return data for visual inspection of the density error.
chemical_potential(occ_root, float][, mu0, …]) Search chemical potential for a given occupation.
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.
density_error2(delta_gf_iw, iw_n) Return an estimate for the upper bound of the error in the density.
density_iw(iws, gf_iw, beta[, weights, …]) Calculate the number density of the Green’s function gf_iw at finite temperature beta.
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.
get_versions() Get version information or return default if unable to do so.
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.
onedim_dos(eps, half_bandwidth) DOS of non-interacting 1D lattice.
onedim_dos_moment(m, half_bandwidth) Calculate the m th moment of the 1D DOS.
onedim_gf_z(z, half_bandwidth) Local Green’s function of the 1D lattice.
onedim_hilbert_transform(xi, half_bandwidth) Hilbert transform of non-interacting DOS of the 1d lattice.
pade_frequencies(num, beta) Return num fermionic Padé frequencies \(iz_p\).
pole_gf_d1_z(z, poles, weights) First derivative of Green’s function given by a finite number of poles.
pole_gf_moments(poles, weights, order) High-frequency moments of the pole Green’s function.
pole_gf_tau(tau, poles, weights, beta) Imaginary time Green’s function given by a finite number of poles.
pole_gf_tau_b(tau, poles, weights, beta) Bosonic 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.
square_dos(eps, half_bandwidth) DOS of non-interacting 2D square lattice.
square_dos_moment(m, half_bandwidth) Calculate the m th moment of the square DOS.
square_gf_z(z, half_bandwidth) Local Green’s function of the 2D square lattice.
square_hilbert_transform(xi, half_bandwidth) Hilbert transform of non-interacting DOS of the square lattice.
surface_gf_zeps(z, eps, hopping_nn) Surface Green’s function for stacked layers.

Classes

Result(x, err)