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: User-accessible input variables
ed_vars_global: Global variable accessible throughout the code
ed_aux_funx: Assortment of auxiliary procedures required throughout the code
ed_setup: Routines for solver environment initialization and finalization
ed_bath: Routines for bath creation and manipulation
ed_greens_functions: Routines for Green's functions calculation
ed_chi_functions: Routines for susceptibilities calculation

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 ed_io/ed_get_gimp(self[, 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:

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

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

Parameters:

self (various shapes) [complex, inout] – Green's function matrix

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[, 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:

[ lmats / lreal]

Parameters:

self (•) [complex, inout] – phonon's Green's function matrix

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[, 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:

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

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

Parameters:

self (various shapes) [complex, inout] – Green's function matrix

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 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:

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

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

The bath is an array having the following dimension:

[nb] for single-impurity DMFT

Where nb is the length of the bath array.

Parameters:

self (various shapes) [complex, inout] – Green's function matrix
bath (•) [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[, 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:

[ lmats / lreal]

Parameters:

self (•, •, •) [complex, inout] – spin susceptibility

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[, 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:

[ lmats / lreal]

Parameters:

self (•, •, •) [complex, inout] – spin susceptibility

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[, 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:

[ lmats / lreal]

Parameters:

self (•, •, •) [complex, inout] – spin susceptibility

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[, 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:

[ lmats / lreal]

Parameters:

self (•, •, •, •) [complex, inout] – spin susceptibility

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[, iorb])

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

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

Parameters:: self (various shapes) [real] – The density value or array of values
Options:: iorb [integer] – the orbital index

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

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 returns given magnetization component for that orbital

[norb]: returns the specified magnetization component for all orbitals

[3 , norb, ]: returns all components for all orbitals

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)

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

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

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

Parameters:: self (various shapes) [real] – double-occupation value or array of values
Options:: iorb [integer] – orbital index

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

This subroutine gets from the EDIpack library the modulus 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]: for single-impurity DMFT, \(\phi\) for all diagonal orbitals

[norb , norb]: for single-impurity DMFT, \(\phi\) for all orbitals

Parameters:

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

Options:

arg (various shapes) [real] – \(\theta\) value or array of values
iorb [integer] – first orbital index
jorb [integer] – second orbital index

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

This subroutine gets from the EDIpack library the argument 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:

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

[norb]: for single-impurity DMFT, \(\theta\) for all diagonal orbitals

[norb , norb]: for single-impurity DMFT, \(\theta\) for all orbitals

Parameters:

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

Options:

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

interface ed_io/ed_get_exct(self, component[, 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:

scalar: if iorb is provided returns \(X\) between orbital and orbital+1 for component

[4]: returns \(X\) for all component and optional orbitals iorb, jorb [default (1,2)].

[norb , norb]: for single-impurity DMFT, \(X\) for all orbitals and component

[4, norb , norb]: for single-impurity DMFT, \(X\) for all orbitals and all component

Parameters:

self (various shapes) [real] – \({S_0,T_x,T_y,T_z}\) value
component [character(len=1)]

Options:

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

interface ed_io/ed_get_eimp(self)

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:

[4]: for single-site DMFT

Parameters:: self (•) [real] – energy components array

interface ed_io/ed_get_epot(self)

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:

scalar: for single-site DMFT

Parameters:: self [real] – value of ed_epot

interface ed_io/ed_get_eint(self)

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:

scalar: for single-site DMFT

Parameters:: self [real] – value of ed_int

interface ed_io/ed_get_ehartree(self)

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:

scalar: for single-site DMFT

Parameters:: self [real] – value of ed_ehartree

interface ed_io/ed_get_eknot(self)

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:

scalar: for single-site DMFT

Parameters:: self [real] – value of ed_eknot

interface ed_io/ed_get_doubles(self)

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:

[4]: for single-site DMFT

Parameters:: self (•) [real] – array of two-body terms expectation values

interface ed_io/ed_get_dust(self)

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:

scalar: for single-site DMFT

Parameters:: self [real] – value of dust

interface ed_io/ed_get_dund(self)

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:

scalar: for single-site DMFT

Parameters:: self [real] – value of dund

interface ed_io/ed_get_dse(self)

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:

scalar: for single-site DMFT

Parameters:: self [real] – value of dse

interface ed_io/ed_get_dph(self)

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:

scalar: for single-site DMFT

Parameters:: self [real] – value of dph

interface ed_io/ed_get_sp_dm(dm[, iprint])

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

[nspin \(\cdot\) norb, nspin\(\cdot\)norb]

Parameters:: dm (various shapes) [complex, out]
Options:: iprint [logical] – ,custom_rot,dm_eig_,dm_rot_)

interface ed_io/ed_get_impurity_rdm(rdm[, doprint])

This subroutine returns to the user the impurity reduced density matrix (RDM). The RDM is an array having the following dimensions:

[\(4^N\) , \(4^N\) ] where \(N\) = Norb

Parameters:: rdm (•, •) [complex, inout]
Options:: doprint [logical, in]

subroutine ed_io/ed_get_imp_info(self)

Parameters:: self (2) [real]
Use :: ed_input_vars (nspin, norb)

subroutine ed_io/ed_get_evals(self)

Parameters:: self (•) [real, allocatable]

function ed_io/ed_get_nsectors()

Result:: n [integer]

subroutine ed_io/ed_get_neigen_sector(nvec)

Parameters:: nvec (nsectors) [integer]

subroutine ed_io/ed_set_neigen_sector(nvec)

Parameters:: nvec (nsectors) [integer]

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