Input / Output Functions

These functions pass to the userspace the observables and response functions calculated and stored within the EDIpack library.

edipack2py.global_env.get_dens(ilat=None, iorb=None)[source]

This function returns the value of the charge density

Parameters:

  • ilat (int) – if the case of real-space DMFT, if only the Green’s function of a specific inequivalent site is needed, this can be specified.

  • iorb (int) – the orbital index. If none is provided, the whole density vector is returned

Returns:

the full charge density tensor has dimensions [ Nlat ,Norb]. Depending on which keyword arguments are (or not) provided, this is sliced on the corresponding axis.

Return type:

float or np.array(dtype=float)

edipack2py.global_env.get_docc(ilat=None, iorb=None)[source]

This function returns the value of the double occupation

Parameters:

  • ilat (int) – if the case of real-space DMFT, if only the Green’s function of a specific inequivalent site is needed, this can be specified.

  • iorb (int) – the orbital index. If none is provided, the whole density vector is returned

Returns:

the full double-occupation tensor has dimensions [ Nlat ,Norb]. Depending on which keyword arguments are (or not) provided, this is sliced on the corresponding axis.

Return type:

float or np.array(dtype=float)

edipack2py.global_env.get_eimp(ilat=None, ikind=None)[source]

This function returns the value of the local energy components

Parameters:

  • ilat (int) – if the case of real-space DMFT, if only the Green’s function of a specific inequivalent site is needed, this can be specified.

  • ikind (int) –

    index of the component. It is

    • 1: ed_Epot: the potential energy from interaction

    • 2: ed_Eint: ed-Epot - ed_Ehartree

    • 3: ed_Ehartree: Hartree part of interaction energy

    • 4: ed_Eknot: on-site part of the kinetic term

Returns:

the full local energy tensor has dimensions [ Nlat ,4]. Depending on which keyword arguments are (or not) provided, this is sliced on the corresponding axis.

Return type:

float or np.array(dtype=float)

edipack2py.global_env.get_mag(icomp=None, ilat=None, iorb=None)[source]

This function returns the value of the magnetization

Parameters:

  • icomp (str) – the component of the magnetization, "x", "y" or "z" (default).

  • ilat (int) – if the case of real-space DMFT, if only the Green’s function of a specific inequivalent site is needed, this can be specified.

  • iorb (int) – the orbital index. If none is provided, the whole density vector is returned

Returns:

the full magnetization tensor has dimensions [ Nlat ,3,Norb]. Depending on which keyword arguments are (or not) provided, this is sliced on the corresponding axis.

Return type:

float or np.array(dtype=float)

edipack2py.global_env.get_phi(ilat=None, iorb=None, jorb=None, component=None)[source]

This function returns the modulus and/or argument of the superconductive order parameter \(\phi = \langle c_{\uparrow} c_{\downarrow} \rangle\)

Parameters:

  • ilat (int) – if the case of real-space DMFT, if only the Green’s function of a specific inequivalent site is needed, this can be specified.

  • iorb (int) – the first orbital index

  • jorb (int) – the second orbital index

  • component (str) – if mod returns the modulus of \(\phi\), if arg returns the argument. By default returns both.

Returns:

\(|\phi|\), \(\mathrm{arg}(\phi)\). The full tensors have dimensions [ Nlat, Norb, Norb]. Depending on which keyword arguments are (or not) provided, this is sliced on the corresponding axis.

Return type:

float or np.array(dtype=float)

edipack2py.global_env.get_gimp(ilat=None, ishape=None, axis='m', typ='n', zeta=None)[source]

This function generates the impurity Green’s function for a user-chosen set of frequencies in the complex plane

Parameters:

  • ilat (int) – if the case of real-space DMFT, if only the self-energy of a specific inequivalent site is needed, this can be specified.

  • ishape (int) –

    this variable determines the shape of the returned array. Possible values:

    • None: the same shape as Hloc plus one axis for frequency

    • 3: in the single-impurity case, it will return an array of the shape [ Nspin \(\cdot\) Norb , Nspin \(\cdot\) Norb , len(zeta) ]. In the real-space DMFT case, it will return an array of the shape [ Nlat \(\cdot\) Nspin \(\cdot\) Norb , Nlat \(\cdot\) Nspin \(\cdot\) Norb , len(zeta) ]. Nlat will be determined from the module by assessing the shape of Hloc. If ilat is set, ValueError is returned.

    • 4: in the real-space DMFT case, it will return an array of the shape [ Nlat , Nspin \(\cdot\) Norb , Nspin \(\cdot\) Norb , len(zeta) . :code:`Nlat will be determined from the module by assessing the shape of Hloc. If ilat is set, the output will have one dimension less.

    • 5: in the single-impurity case, it will return an array of the shape [ Nspin , Nspin , Norb , Norb , len(zeta) ].

    • 6: in the real-space DMFT case, it will return an array of the shape [ Nlat , Nspin , Nspin , Norb , Norb , len(zeta) ]. Nlat will be determined from the module by assessing the shape of Hloc. If ilat is set, the output will have one dimension less.

  • axis (str) – if zeta is not provided, return the self-energy on the Matsubara or Real axis with parameters set in the input file. Can be m for Matsubara(default) or r for real.

  • typ (str) – whether to return the normal or anomalous self-energy (for the superconducting case). Can be n for normal (default) or a for anomalous.

  • zeta (complex or [complex] or np.array(dtype=complex)) – user-defined array of frequencies in the whole complex plane. If none is provided, according to axis the Matsubara or real axis is chosen

Raises:

  • ValueError – If ishape is incompatible woth ilat or not in the previous list.

  • ValueError – If axis is not in the previous list.

Returns:

An array of floats that contains the impurity Green’s function along the specific axis, with dimension set by ishape and zeta, if present.

Return type:

np.array(dtype=float)

edipack2py.global_env.get_sigma(ilat=None, ishape=None, axis='m', typ='n', zeta=None)[source]

This function generates the self-energy for a user-chosen set of frequencies in the complex plane

Parameters:

  • ilat (int) – if the case of real-space DMFT, if only the self-energy of a specific inequivalent site is needed, this can be specified.

  • ishape (int) –

    this variable determines the shape of the returned array. Possible values:

    • None: the same shape as Hloc plus one axis for frequency

    • 3: in the single-impurity case, it will return an array of the shape [ Nspin \(\cdot\) Norb , Nspin \(\cdot\) Norb , len(zeta) ]. In the real-space DMFT case, it will return an array of the shape [ Nlat \(\cdot\) Nspin \(\cdot\) Norb , Nlat \(\cdot\) Nspin \(\cdot\) Norb , len(zeta) ]. Nlat will be determined from the module by assessing the shape of Hloc. If ilat is set, ValueError is returned.

    • 4: in the real-space DMFT case, it will return an array of the shape [ Nlat , Nspin \(\cdot\) Norb , Nspin \(\cdot\) Norb , len(zeta) . :code:`Nlat will be determined from the module by assessing the shape of Hloc. If ilat is set, the output will have one dimension less.

    • 5: in the single-impurity case, it will return an array of the shape [ Nspin , Nspin , Norb , Norb , len(zeta) ].

    • 6: in the real-space DMFT case, it will return an array of the shape [ Nlat , Nspin , Nspin , Norb , Norb , len(zeta) ]. Nlat will be determined from the module by assessing the shape of Hloc. If ilat is set, the output will have one dimension less.

  • axis (str) – if zeta is not provided, return the self-energy on the Matsubara or Real axis with parameters set in the input file. Can be m for Matsubara(default) or r for real.

  • typ (str) – whether to return the normal or anomalous self-energy (for the superconducting case). Can be n for normal (default) or a for anomalous.

  • zeta (complex or [complex] or np.array(dtype=complex)) – user-defined array of frequencies in the whole complex plane. If none is provided, according to axis the Matsubara or real axis is chosen

Raises:

  • ValueError – If ishape is incompatible woth ilat or not in the previous list.

  • ValueError – If axis is not in the previous list.

Returns:

An array of floats that contains the self-energy along the specific axis, with dimension set by ishape and zeta, if present.

Return type:

np.array(dtype=float)

edipack2py.global_env.get_g0and(zeta, bath, ishape=None, typ='n')[source]

This function calculates the value of the Anderson Impurity Model’s noninteracting Green’s function on a given frequency array.

Parameters:

  • zeta (complex) – the array of frequencies (only frequencies on the real and imaginary axes are supported)

  • bath (float) – the user-accessible bath array

  • ishape (int) –

    this variable determines the shape of the returned array. Possible values:

    • None: the same shape as Hloc plus one axis for frequency

    • 3: the output array will have shape [ Nspin \(\cdot\) Norb , Nspin \(\cdot\) Norb , len(zeta) ]

    • 5: the output array will have shape [ Nspin , Nspin , Norb , Norb , len(zeta) ]

  • typ (str) – whether to return the normal or anomalous Green’s function (for the superconducting case). Can be n for normal or a for anomalous.

Raises:

  • ValueError – If zeta is not completely real or completely imaginary

  • ValueError – If ishape is not 3 or 5.

Returns:

An array of complex that contains \(G^{And}_{0}(z)\) function along the specific frequency array, with dimension set by ishape and zeta.

Return type:

np.array(dtype=complex)

edipack2py.global_env.get_delta(zeta, bath, ishape=None, typ='n')[source]

This function calculates the value of the Anderson Impurity Model’s hybridization function on a given frequency array.

Parameters:

  • zeta (complex) – the array of frequencies (only frequencies on the real and imaginary axes are supported)

  • bath (float) – the user-accessible bath array

  • ishape (int) –

    this variable determines the shape of the returned array. Possible values:

    • None: the same shape as Hloc plus one axis for frequency

    • 3: the output array will have shape [ Nspin \(\cdot\) Norb , Nspin \(\cdot\) Norb , len(zeta) ]

    • 5: the output array will have shape [ Nspin , Nspin , Norb , Norb , len(zeta) ]

  • typ (str) – whether to return the normal or anomalous Green’s function (for the superconducting case). Can be n for normal or a for anomalous.

Raises:

  • ValueError – If zeta is not completely real or completely imaginary

  • ValueError – If ishape is not 3 or 5.

Returns:

An array of complex that contains \(\Delta(z)\) along the specific frequency array, with dimension set by ishape and zeta.

Return type:

np.array(dtype=complex)

edipack2py.global_env.get_chi(chan='spin', zeta=None, axis=None, ilat=None)[source]

This function calculates the value of the Anderson Impurity Model’s response functions \(\chi\) in the spin, density, pairing and exciton channels.

Parameters:

  • chan (str) – the channel of the response function. Possible values are spin ( s ), dens ( c ), pair ( p ), exct ( e ). Default is spin.

  • zeta (complex) – the array of frequencies or times (only frequencies on the real imaginary axes and imaginary times are supported). If no array is provided, depending on the value of axis, an array will be generated on the positive Matsubara axis ( Lmats values ), on the real axis ( Lreal values between 0 and wfin) or on the imaginary time axis (Ltau values between 0 and beta)

  • axis (str) – the axis on which to calculate \(\chi\). Possible values matsubara ( m), real ( r), time ( t). This parameter has to be specificed.

  • ilat (int) – for real-space DMFT, if this flag is specified only the susceptibility for the relative inequivalent atom is returned specified.

Raises:
Returns:

An array of complex that contains \(\chi\) along the chosen axis. The dimension of the array depends on the chosen channel:

  • [ Norb, Norb , len(zeta) ] for channel spin, dens, pair

  • [ 3, Norb, Norb , len(zeta) ] for channel exct, corresponding to singlet, triplet(xy) and triplet(z)

One dimension corresponding to the number of inequivalent sites is added at the beginning for the case of real-space DMFT and if ilat is None.

Return type:

np.array(dtype=complex)

edipack2py.global_env.get_impurity_rdm(doprint=False)[source]

This function returns the impurity reduced density matrix (iRDM)

Parameters:

doprint (bool) – if True, the RDM is printed to file.

Returns:

the impurity density matrix, a square matrix of size \(4^{N_{orb}}\times 4^{N_{orb}}\)

Return type:

np.array(dtype=complex)