Input / Output Functions

Description

Contains a set of routines that retrieve quantities such as Green's functions, self-energies (see ed_greens_functions ) and observables (from ed_observables ) and pass them to the user, as well ass routines to read and store Green's function and self-energies.

Quick access

Used modules

edipack: EDIpack library frontend
e2i_vars_global: Global variables, inequivalent sites version
e2i_aux_funx: Assortment of auxiliary procedures, inequivalent sites version

External modules

sf_linalg
sf_spin
sf_arrays
- linspace()
- arange()
sf_iotools
- str()
- reg()
- free_unit()
- splot()
- sread()
sf_misc
- assert_shape()

Subroutines and functions

interface e2i_io/ed_get_gimp(self, nlat[, axis, type, z])

This subroutine gets from the EDIpack library the value of the impurity Green's function calculated on the Matsubara or real-frequency axis, with number of frequencies lmats or lreal .

The impurity Green's function is an array having the following possible dimensions:

[nlat \(\cdot\) nspin \(\cdot\) norb, nlat \(\cdot\) nspin \(\cdot\) norb, lmats / lreal]

[nlat, nspin \(\cdot\) norb, nspin \(\cdot\) norb, lmats / lreal]

[nlat, nspin, nspin, norb, norb, lmats / lreal]

Parameters:

self (various shapes) [complex, inout] – [Nlso,Nlso,:]
nlat [integer, in] – Number of inequivalent impurity sites for real-space DMFT

Options:

axis [character(len=*)] – Can be "m" for Matsubara (default), "r" for real
type [character(len=*)] – Can be "n" for Normal (default), "a" for anomalous
z (•) [complex] – User provided array of complex frequency where to evaluate Self

interface e2i_io/ed_get_dimp(self, nlat[, axis, z])

This subroutine gets from the EDIpack library the value of the impurity phonon's Green's function calculated on the Matsubara or real-frequency axis, with number of frequencies lmats or lreal .

The impurity phonon's Green's function is an array having the following possible dimensions:

[nlat, lmats / lreal]

Parameters:

self (•, •) [complex, inout] – [Nlso,Nlso,:]
nlat [integer, in] – Number of inequivalent impurity sites for real-space DMFT

Options:

axis [character(len=*)] – Can be "m" for Matsubara (default), "r" for real
z (•) [complex] – User provided array of complex frequency where to evaluate Self

interface e2i_io/ed_get_sigma(self, nlat[, axis, type, z])

This subrotine gets from the EDIpack library the value of the self-energy calculated on the Matsubara or real-frequency axis, with number of frequencies lmats or lreal .

The self-energy is an array having the following possible dimensions:

[nlat \(\cdot\) nspin \(\cdot\) norb, nlat \(\cdot\) nspin \(\cdot\) norb, lmats / lreal]

[nlat, nspin \(\cdot\) norb, nspin \(\cdot\) norb, lmats / lreal]

[nlat, nspin, nspin, norb, norb, lmats / lreal]

Parameters:

self (various shapes) [complex, inout] – [Nlso,Nlso,:]
nlat [integer, in] – Number of inequivalent impurity sites for real-space DMFT

Options:

axis [character(len=*)] – Can be "m" for Matsubara (default), "r" for real
type [character(len=*)] – Can be "n" for Normal (default), "a" for anomalous
z (•) [complex] – User provided array of complex frequency where to evaluate Self

interface e2i_io/ed_get_g0imp(self, bath[, axis, type, z])

This subroutine gets from the EDIpack library the value of the impurity non-interacting Green's function calculated on the Matsubara or real-frequency axis, with number of frequencies lmats or lreal .

It autonomously decides whether the system is single-impurity or real-space DMFT based on the bath shape

The impurity non-interacting Green's function is an array having the following possible dimensions:

[nlat \(\cdot\) nspin \(\cdot\) norb, nlat \(\cdot\) nspin \(\cdot\) norb, lmats / lreal]

[nlat, nspin \(\cdot\) norb, nspin \(\cdot\) norb, lmats / lreal]

[nlat, nspin, nspin, norb, norb, lmats / lreal]

The bath is an array having the following possible dimensions:

[nlat, nb] for real-space DMFT, with nlat the number of inequivalent impurity sites

Where nb is the length of the bath array.

Parameters:

self (various shapes) [complex, inout] – [Nlso,Nlso,:]
bath (•, •) [real]

Options:

axis [character(len=*)] – Can be "m" for Matsubara (default), "r" for real
type [character(len=*)] – Can be "n" for Normal (default), "a" for anomalous
z (•) [complex] – User provided array of complex frequency where to evaluate Self

interface e2i_io/ed_get_spinchi(self, nlat[, axis, z])

This subroutine gets from the EDIpack library the value of the impurity spin susceptibility function calculated on the Matsubara or real-frequency axis, with number of frequencies lmats or lreal .

The impurity spin susceptibility function is an array having the following possible dimensions:

[nlat, lmats / lreal]

Parameters:

self (•, •, •, •) [complex, inout] – [Nlat,Norb,Norb,:]
nlat [integer, in] – Number of inequivalent impurity sites for real-space DMFT

Options:

axis [character(len=*)] – Can be "m" for Matsubara (default), "r" for real
z (•) [complex] – User provided array of complex frequency where to evaluate Self

interface e2i_io/ed_get_denschi(self, nlat[, axis, z])

This subroutine gets from the EDIpack library the value of the impurity dens susceptibility function calculated on the Matsubara or real-frequency axis, with number of frequencies lmats or lreal .

The impurity dens susceptibility function is an array having the following possible dimensions:

[nlat, lmats / lreal]

Parameters:

self (•, •, •, •) [complex, inout] – [Nlat,Norb,Norb,:]
nlat [integer, in] – Number of inequivalent impurity sites for real-space DMFT

Options:

axis [character(len=*)] – Can be "m" for Matsubara (default), "r" for real
z (•) [complex] – User provided array of complex frequency where to evaluate Self

interface e2i_io/ed_get_pairchi(self, nlat[, axis, z])

This subroutine gets from the EDIpack library the value of the impurity pair susceptibility function calculated on the Matsubara or real-frequency axis, with number of frequencies lmats or lreal .

The impurity pair susceptibility function is an array having the following possible dimensions:

[nlat, lmats / lreal]

Parameters:

self (•, •, •, •) [complex, inout] – [Nlat,Norb,Norb,:]
nlat [integer, in] – Number of inequivalent impurity sites for real-space DMFT

Options:

axis [character(len=*)] – Can be "m" for Matsubara (default), "r" for real
z (•) [complex] – User provided array of complex frequency where to evaluate Self

interface e2i_io/ed_get_exctchi(self, nlat[, axis, z])

This subroutine gets from the EDIpack library the value of the impurity exct susceptibility function calculated on the Matsubara or real-frequency axis, with number of frequencies lmats or lreal .

The impurity exct susceptibility function is an array having the following possible dimensions:

[nlat, lmats / lreal]

Parameters:

self (•, •, •, •, •) [complex, inout] – [Nlat,3,Norb,Norb,:]
nlat [integer, in] – Number of inequivalent impurity sites for real-space DMFT

Options:

axis [character(len=*)] – Can be "m" for Matsubara (default), "r" for real
z (•) [complex] – User provided array of complex frequency where to evaluate Self

interface e2i_io/ed_get_dens(self, nlat)

This subroutine gets from the EDIpack library the value of the charge density and passes it to the user.

The self variable can have the following dimensions:

scalar: if iorb is provided for single-impurity DMFT, density for that orbital

[nlat]: if iorb (default = 1) is provided for real-space DMFT with nlat impurities, density for that orbital for all impurity sites

[nlat, norb]: if nlat is provided for real-space DMFT, density for all impurity sites and orbitals

Parameters:

self (various shapes) [real]
nlat [integer]

interface e2i_io/ed_get_mag(self, nlat[, component])

This subroutine gets from the EDIpack library the value of the magnetization and passes it to the user.

The self variable can have the following dimensions:

scalar: if component and iorb are provided for single-impurity DMFT, given magnetization component for that orbital

[nlat]: for real-space DMFT with nlat impurities, magnetization for that orbital for all impurity sites

[nlat, norb]: if nlat is provided for real-space DMFT, one magnetization component for all orbitals and impurity sites

[nlat, 3, norb]: if nlat is provided for real-space DMFT, all magnetization components for all orbitals and sites

Parameters:

self (various shapes) [real]
nlat [integer]

Options:

component [character(len=1)]

interface e2i_io/ed_get_docc(self, nlat)

This subroutine gets from the EDIpack library the value of the double occupation and passes it to the user.

The self variable can have the following dimensions:

scalar: if iorb is provided for single-impurity DMFT, dobule-occupation for that orbital

[nlat]: if iorb (default = 1) is provided for real-space DMFT with nlat impurities, double-occupation for that orbital for all impurity sites

[nlat, norb]: if nlat is provided for real-space DMFT, double-occupation for all impurity sites and orbitals

Parameters:

self (various shapes) [real]
nlat [integer]

interface e2i_io/ed_get_phi(self, nlat[, arg])

This subroutine gets from the EDIpack library the modulus value of the superconducting order parameter \(\phi\) ( ed_mode = superc ) and passes it to the user.

The self variable can have the following dimensions:

[nlat]: \(\phi\) for the specified iorb orbital and all impurity sites

[nlat, norb]: \(\phi\) for all impurity sites and orbitals

Parameters:

self (various shapes) [real]
nlat [integer]

Options:

arg (various shapes) [real]

interface e2i_io/ed_get_argphi(self, nlat)

This subroutine gets from the EDIpack library the argument value of the superconducting order parameter \(\theta=tan^{-1}(Im\phi/Re\phi)\) ( ed_mode = superc ) and passes it to the user.

The self variable can have the following dimensions:

[nlat]: \(\theta\) for the specified iorb orbital and all impurity sites

[nlat, norb]: \(\theta\) for all impurity sites and orbitals

Parameters:

self (various shapes) [real]
nlat [integer]

interface e2i_io/ed_get_exct(self, nlat[, iorb, jorb])

This subroutine gets from the EDIpack library the value of the excitonic order parameters \(X^a\) ( ed_mode = normal,:code:nonsu2 ) and passes it to the user.

The self variable can have the following dimensions:

[nlat]: if iorb is provided \(X\) between orbital and orbital+1 for component and and all impurity sites

[nlat , norb , norb]: \(X\) for all orbitals, for component and all impurity sites.

[nlat , 4, norb , norb]: \(X\) for all orbitals, component and all impurity sites.

Parameters:

self (various shapes) [real] – \([S_0,T_x,T_y,T_z]\) array
nlat [integer]

Options:

iorb [integer] – first orbital index
jorb [integer] – second orbital index

interface e2i_io/ed_get_eimp(self, nlat)

This subroutine gets from the EDIpack library and passes to the user the array [ ed_epot , ed_eint , ed_ehartree , ed_eknot ]. These are the expectation values various contribution to the internal energy

ed_epot = energy contribution from the interaction terms, including the Hartree term

ed_eint = energy contribution from the interaction terms, excluding the Hartree term

ed_ehartree = \(-\frac{U}{2} \sum_{i} \langle n_{i\uparrow} + n_{i\downarrow} \rangle -\frac{2U^{'}-J_{H}}{2} \sum_{i < j} \langle n_{i\uparrow}+n_{i\downarrow} + n_{i\downarrow}+n_{j\downarrow} \rangle +\frac{U}{4} + \frac{2U^{'}-J_{H}}{2}\) for \(i,j\) orbitals

ed_eknot = kinetic term from the local 1-body Hamiltonian

The returned array can have the following dimensions:

[nlat, 4]: for real-space DMFT with nlat impurities

Parameters:

self (•, •) [real]
nlat [integer] – number of inequivalent impurity sites for real-space DMFT

interface e2i_io/ed_get_epot(self, nlat)

This subroutine gets from the EDIpack library and passes to the user the value of ed_epot, the energy contribution from the interaction terms, including the Hartree term. The returned array can have the following dimensions:

[nlat]: for real-space DMFT with nlat impurities

Parameters:

self (•) [real]
nlat [integer] – number of inequivalent impurity sites for real-space DM

interface e2i_io/ed_get_eint(self, nlat)

This subroutine gets from the EDIpack library and passes to the user the value of ed_int, the energy contribution from the interaction terms, excluding the Hartree term. The returned array can have the following dimensions:

[nlat]: for real-space DMFT with nlat impurities

Parameters:

self (•) [real]
nlat [integer] – number of inequivalent impurity sites for real-space DM

interface e2i_io/ed_get_ehartree(self, nlat)

This subroutine gets from the EDIpack library and passes to the user the value of the Hartree potential ed_ehartree. The returned array can have the following dimensions:

[nlat]: for real-space DMFT with nlat impurities

Parameters:

self (•) [real]
nlat [integer] – number of inequivalent impurity sites for real-space DM

interface e2i_io/ed_get_eknot(self, nlat)

This subroutine gets from the EDIpack library and passes to the user the value ed_eknot, the kinetic term from the local 1-body Hamiltonian The returned array can have the following dimensions:

[nlat]: for real-space DMFT with nlat impurities

Parameters:

self (•) [real]
nlat [integer] – number of inequivalent impurity sites for real-space DM

interface e2i_io/ed_get_doubles(self, nlat)

This subroutine gets from the EDIpack library and passes to the user the array [ ed_dust , ed_dund , ed_dse , ed_dph ]. These are the expectation values of the two-body operators associated with the density-density inter-orbital interaction (with opposite and parallel spins), spin-exchange and pair-hopping.

ed_dust = \(\sum_{i < j} n_{i\uparrow}n_{j\downarrow} + n_{i\downarrow}n_{j\uparrow}\) for \(i,j\) orbitals

ed_dund = \(\sum_{i < j} n_{i\uparrow}n_{j\uparrow} + n_{i\downarrow}n_{j\downarrow}\) for \(i,j\) orbitals

ed_dse = \(\sum_{i < j} c^{\dagger}_{i\uparrow}c^{\dagger}_{j\uparrow}c_{i\downarrow}c_{j\uparrow}\) for \(i,j\) orbitals

ed_dph = \(\sum_{i < j} c^{\dagger}_{i\uparrow}c^{\dagger}_{i\downarrow}c_{j\downarrow}c_{j\uparrow}\) for \(i,j\) orbitals

The returned array can have the following dimensions:

[nlat, 4]: for real-space DMFT with nlat impurities

Parameters:

self (•, •) [real]
nlat [integer] – number of inequivalent impurity sites for real-space DMFT

interface e2i_io/ed_get_dust(self, nlat)

This subroutine gets from the EDIpack library and passes to the user the value of ed_dust = \(\sum_{i < j} n_{i\uparrow}n_{j\downarrow} + n_{i\downarrow}n_{j\uparrow}\) for \(i,j\) orbitals The returned array can have the following dimensions:

[nlat]: for real-space DMFT with nlat impurities

Parameters:

self (•) [real]
nlat [integer] – number of inequivalent impurity sites for real-space DMFT

interface e2i_io/ed_get_dund(self, nlat)

This subroutine gets from the EDIpack library and passes to the user the value of ed_dund = \(\sum_{i < j} n_{i\uparrow}n_{j\uparrow} + n_{i\downarrow}n_{j\downarrow}\) for \(i,j\) orbitals The returned array can have the following dimensions:

[nlat]: for real-space DMFT with nlat impurities

Parameters:

self (•) [real]
nlat [integer] – number of inequivalent impurity sites for real-space DMFT

interface e2i_io/ed_get_dse(self, nlat)

This subroutine gets from the EDIpack library and passes to the user the value of ed_dse = \(\sum_{i < j} c^{\dagger}_{i\uparrow}c^{\dagger}_{j\uparrow}c_{i\downarrow}c_{j\uparrow}\) for \(i,j\) orbitals The returned array can have the following dimensions:

[nlat]: for real-space DMFT with nlat impurities

Parameters:

self (•) [real]
nlat [integer] – number of inequivalent impurity sites for real-space DMFT

interface e2i_io/ed_get_dph(self, nlat)

This subroutine gets from the EDIpack library and passes to the user the value of ed_dph = \(\sum_{i < j} c^{\dagger}_{i\uparrow}c^{\dagger}_{i\downarrow}c_{j\downarrow}c_{j\uparrow}\) for \(i,j\) orbitals The returned array can have the following dimensions:

[nlat]: for real-space DMFT with nlat impurities

Parameters:

self (•) [real]
nlat [integer] – number of inequivalent impurity sites for real-space DMFT