gftool¶
Collection of commonly used Green’s functions and utilities.
Main purpose is to have a tested base.
Submodules¶
gftool.beb |
Blackman, Esterling, and Berk (BEB) approach to off-diagonal disorder. |
gftool.cpa |
Coherent cluster approximation (CPA) to substitutional disorder. |
gftool.fourier |
Fourier transformations of Green’s functions. |
gftool.lattice |
Collection of different lattices and their Green’s functions. |
gftool.matrix |
Functions to work with Green’s functions in matrix from. |
gftool.pade |
Pade analytic continuation for Green’s functions and self-energies. |
gftool.siam |
Basic functions for the (non-interacting) single impurity Anderson model (SIAM). |
Glossary¶
- DOS
- Density of States
- eps
- epsilon
- ϵ
- epsilon
- (Real) energy variable. Typically used for for the DOS where it replaces the k-dependent Dispersion \(ϵ_k\).
- iv
- iν_n
- Bosonic Matsubara frequencies
- iw
- iω_n
- Fermionic Matsubara frequencies
- tau
- τ
- Imaginary time points
- z
- Complex frequency variable
Green’s functions and lattices¶
1D
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. |
2D
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. |
triangular_dos (eps, half_bandwidth) |
DOS of non-interacting 2D triangular lattice. |
triangular_dos_moment (m, half_bandwidth) |
Calculate the m th moment of the triangular DOS. |
triangular_gf_z (z, half_bandwidth) |
Local Green’s function of the 2D triangular lattice. |
triangular_hilbert_transform (xi, half_bandwidth) |
Hilbert transform of non-interacting DOS of the triangular lattice. |
honeycomb_dos (eps, half_bandwidth) |
DOS of non-interacting 2D honeycomb lattice. |
honeycomb_dos_moment (m, half_bandwidth) |
Calculate the m th moment of the honeycomb DOS. |
honeycomb_gf_z (z, half_bandwidth) |
Local Green’s function of the 2D honeycomb lattice. |
honeycomb_hilbert_transform (xi, half_bandwidth) |
Hilbert transform of non-interacting DOS of the honeycomb lattice. |
3D
sc_dos (eps[, half_bandwidth]) |
Local Green’s function of 3D simple cubic lattice. |
sc_dos_moment (m, half_bandwidth) |
Calculate the m th moment of the simple cubic DOS. |
sc_gf_z (z[, half_bandwidth]) |
Local Green’s function of 3D simple cubic lattice. |
sc_hilbert_transform (xi[, half_bandwidth]) |
Hilbert transform of non-interacting DOS of the simple cubic lattice. |
bcc_dos (eps, half_bandwidth) |
DOS of non-interacting 3D body-centered cubic lattice. |
bcc_dos_moment (m, half_bandwidth) |
Calculate the m th moment of the body-centered cubic DOS. |
bcc_gf_z (z, half_bandwidth) |
Local Green’s function of 3D body-centered cubic (bcc) lattice. |
bcc_hilbert_transform (xi, half_bandwidth) |
Hilbert transform of non-interacting DOS of the body-centered cubic lattice. |
fcc_dos (eps, half_bandwidth) |
DOS of non-interacting 3D face-centered cubic lattice. |
fcc_dos_moment (m, half_bandwidth) |
Calculate the m th moment of the face-centered cubic DOS. |
fcc_gf_z (z, half_bandwidth) |
Local Green’s function of the 3D face-centered cubic (fcc) lattice. |
fcc_hilbert_transform (xi, half_bandwidth) |
Hilbert transform of non-interacting DOS of the face-centered cubic lattice. |
Miscellaneous
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_z (z, half_bandwidth) |
Local Green’s function of Bethe lattice for infinite coordination number. |
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_hilbert_transform (xi, half_bandwidth) |
Hilbert transform of non-interacting DOS of the Bethe lattice. |
pole_gf_z (z, poles, weights) |
Green’s function given by a finite number of poles. |
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_ret_t (tt, poles, weights) |
Retarded time Green’s function given by a finite number of poles. |
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. |
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. |
surface_gf_zeps (z, eps, hopping_nn) |
Surface Green’s function for stacked layers. |
Statistics and particle numbers¶
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. |
bose_fct (eps, beta) |
Return the Bose function 1/(exp(βϵ)-1). |
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. |
pade_frequencies (num, beta) |
Return num fermionic Padé frequencies \(iz_p\). |
density_iw (iws, gf_iw, beta[, weights, …]) |
Calculate the number density of the Green’s function gf_iw at finite temperature beta. |
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. |
check_convergence (gf_iw, potential, beta[, …]) |
Return data for visual inspection of the density error. |
Utilities¶
Functions
get_versions () |
Get version information or return default if unable to do so. |
Classes
Result (x, err) |