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

ed_input_vars: Contains all global input variables which can be set by the user through the input file. A specific preocedure ed_read_input() should be called to read the input file using parse_input_variable() procedure from SciFortran. All variables are automatically set to a default, looked for and updated by reading into the file and, sequentially looked for and updated from command line (std.input) using the notation variable_name=variable_value(s) (case independent).
ed_vars_global: Contains all variables, arrays and derived types instances shared throughout the code. Specifically, it contains definitions of the effective_bath, the gfmatrix and the sector data structures.
ed_aux_funx: Hosts a number of auxiliary procedures required in different parts of the code. Specifically, it implements: creation/annihilation fermionic operators, binary decomposition of integer representation of Fock states and setup the local impurity Hamiltonian
ed_setup: Contains procedures to set up the Exact Diagonalization calculation, executing all internal consistency checks and allocation of the global memory.
ed_bath: Contains routines for setting, accessing, manipulating and clearing the bath of the Impurity problem.
ed_greens_functions
ed_chi_functions
sf_linalg
sf_spin
sf_arrays
- linspace()
- arange()
sf_iotools
- str()
- reg()
- free_unit()
- splot()
- sread()
sf_misc
- assert_shape()

Subroutines and functions

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

This subroutine gets from the EDIpack2 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:

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

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

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

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

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

Parameters:

self (various shapes) [complex, inout] – Green’s function matrix
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 ed_io/ed_get_dimp(self, nlat[, axis, z])

This subroutine gets from the EDIpack2 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:

[ lmats / lreal]

[nlat, lmats / lreal]

Parameters:

self (various shapes) [complex, inout] – phonon’s Green’s function matrix
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 ed_io/ed_get_sigma(self, nlat[, axis, type, z])

This subrotine gets from the EDIpack2 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:

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

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

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

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

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

Parameters:

self (various shapes) [complex, inout] – Green’s function matrix
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 ed_io/ed_get_g0imp(self, bath[, axis, type, z])

This subroutine gets from the EDIpack2 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:

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

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

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

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

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

The bath is an array having the following possible dimensions:

[nb] for single-impurity DMFT

[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] – Green’s function matrix
bath (various shapes) [real] – The bath vector

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

This subroutine gets from the EDIpack2 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:

[ lmats / lreal]

[nlat, lmats / lreal]

Parameters:

self (various shapes) [complex, inout] – spin susceptibility
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 ed_io/ed_get_denschi(self, nlat[, axis, z])

This subroutine gets from the EDIpack2 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:

[ lmats / lreal]

[nlat, lmats / lreal]

Parameters:

self (various shapes) [complex, inout] – spin susceptibility
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 ed_io/ed_get_pairchi(self, nlat[, axis, z])

This subroutine gets from the EDIpack2 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:

[ lmats / lreal]

[nlat, lmats / lreal]

Parameters:

self (various shapes) [complex, inout] – spin susceptibility
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 ed_io/ed_get_exctchi(self, nlat[, axis, z])

This subroutine gets from the EDIpack2 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:

[ lmats / lreal]

[nlat, lmats / lreal]

Parameters:

self (various shapes) [complex, inout] – spin susceptibility
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 ed_io/ed_get_dens(self, nlat[, iorb, nlat])

This subroutine gets from the EDIpack2 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:

[ lmats / lreal]

[nlat, lmats / lreal]

Parameters:

self (various shapes) [real] – The density value or array of values

Options:

iorb [integer] – the orbital index
nlat [integer] – the number of inequivalent impurity sites for real-space DMFT

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

This subroutine gets from the EDIpack2 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

[norb]: for single-impurity DMFT, one magnetization component for all orbitals

[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] – Magnetization

Options:

component [character(len=1)] – Component of the magnetization, can be "x", "y", "z" (default "z" )
iorb [integer] – Orbital (default 1)
nlat [integer] – Number of inequivalent impurities for real-space DMFT

interface ed_io/ed_get_docc(self, nlat[, iorb, nlat])

This subroutine gets from the EDIpack2 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

[norb]: if no optional variable is provided for single-impurity DMFT, double-occupation for all orbitals

[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] – double-occupation value or array of values

Options:

iorb [integer] – orbital index
nlat [integer] – number of inequivalent impurity sites for real-space DMFT

interface ed_io/ed_get_phi(self, nlat[, iorb, jorb, nlat])

This subroutine gets from the EDIpack2 library the value of the superconducting order parameter \(\phi\) ( ed_mode = superc ) and passes it to the user.

The self variable can have the following dimensions:

scalar: if iorb is provided for single-impurity DMFT, \(\phi\) for that orbital

[norb]: if no optional variable is provided for single-impurity DMFT, \(\phi\) for all orbitals

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

[nlat, norb]: if nlat is provided for real-space DMFT, \(\phi\) for all impurity sites and orbitals

Parameters:

self (various shapes) [real] – \(\phi\) value or array of values

Options:

iorb [integer] – first orbital index
jorb [integer] – second orbital index
nlat [integer] – number of inequivalent impurity sites for real-space DMFT

interface ed_io/ed_get_eimp(self, nlat)

This subroutine gets from the EDIpack2 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:

[4]: for single-site DMFT

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

Parameters:

self (various shapes) [real] – energy components array
nlat [integer] – number of inequivalent impurity sites for real-space DMFT

interface ed_io/ed_get_epot(self, nlat)

This subroutine gets from the EDIpack2 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:

scalar: for single-site DMFT

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

Parameters:

self (various shapes) [real] – value of ed_epot
nlat [integer] – number of inequivalent impurity sites for real-space DM

interface ed_io/ed_get_eint(self, nlat)

This subroutine gets from the EDIpack2 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:

scalar: for single-site DMFT

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

Parameters:

self (various shapes) [real] – value of ed_int
nlat [integer] – number of inequivalent impurity sites for real-space DM

interface ed_io/ed_get_ehartree(self, nlat)

This subroutine gets from the EDIpack2 library and passes to the user the value of the Hartree potential ed_ehartree. The returned array can have the following dimensions:

scalar: for single-site DMFT

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

Parameters:

self (various shapes) [real] – value of ed_ehartree
nlat [integer] – number of inequivalent impurity sites for real-space DM

interface ed_io/ed_get_eknot(self, nlat)

This subroutine gets from the EDIpack2 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:

scalar: for single-site DMFT

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

Parameters:

self (various shapes) [real] – value of ed_eknot
nlat [integer] – number of inequivalent impurity sites for real-space DM

interface ed_io/ed_get_doubles(self, nlat)

This subroutine gets from the EDIpack2 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:

[4]: for single-site DMFT

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

Parameters:

self (various shapes) [real] – array of two-body terms expectation values
nlat [integer] – number of inequivalent impurity sites for real-space DMFT

interface ed_io/ed_get_dust(self, nlat)

This subroutine gets from the EDIpack2 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:

scalar: for single-site DMFT

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

Parameters:

self (various shapes) [real] – value of dust
nlat [integer] – number of inequivalent impurity sites for real-space DMFT

interface ed_io/ed_get_dund(self, nlat)

This subroutine gets from the EDIpack2 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:

scalar: for single-site DMFT

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

Parameters:

self (various shapes) [real] – value of dund
nlat [integer] – number of inequivalent impurity sites for real-space DMFT

interface ed_io/ed_get_dse(self, nlat)

This subroutine gets from the EDIpack2 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:

scalar: for single-site DMFT

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

Parameters:

self (various shapes) [real] – value of dse
nlat [integer] – number of inequivalent impurity sites for real-space DMFT

interface ed_io/ed_get_dph(self, nlat)

This subroutine gets from the EDIpack2 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:

scalar: for single-site DMFT

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

Parameters:

self (various shapes) [real] – value of dph
nlat [integer] – number of inequivalent impurity sites for real-space DMFT

interface ed_io/ed_get_sp_dm(dm_)

This subroutine returns to the user the impurity density matrix. The density matrix is an array having the following possible dimensions:

[nspin \(\cdot\) norb, nspin\(\cdot\)norb] for single-impurity DMFT

[nlat, nspin \(\cdot\) norb, nspin\(\cdot\)norb] for real-space DMFT

Parameters:: dm_ (various shapes) [complex, out,allocatable] – ,custom_rot,dm_eig_,dm_rot_)

subroutine ed_io/ed_get_imp_info(self)

Parameters:: self (2) [real]

subroutine ed_io/ed_get_quantum_soc_operators(): This subroutine gets and prints the values of the components \(\overrightarrow{L}\), \(\overrightarrow{S}\), \(\overrightarrow{J}\) in the chosen basis depending on jz_basis, and prints them on the files "L_imp_"//reg(str(ndx))//".dat" , "S_imp_"//reg(str(ndx))//".dat" and "J_imp_"//reg(str(ndx))//".dat" , where ndx is the inequivalent impurity site for real-space DMFT (if that is the case). The ordering of the results in the output files is described by comments in the files themselves

subroutine ed_io/ed_get_neigen_total(nlii, nlat)

In the case of inequivalent impurity sites, this function returns the number of eigenstates per impurity site in the ED spectrum.

Parameters:: nlii (nlat) [integer] – array containing the number of eigenstates per inequivalent impurity site
Options:: nlat [integer] – number of inequivalent impurity sites for real-space DMFT