Many-Body Properties

Purpose: Green's functions, self-energies, hybridization, quasiparticle weights, hopping matrices

In scope:

• Green's function base class and electronic specialization
• Self-energies from GW and DMFT
• Hybridization functions for impurity problems
• Quasiparticle renormalization weights
• Hopping matrices from tight-binding
• Crystal field splittings in correlated systems

Relationship map

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classDiagram
    class BaseGreensFunction
    class CrystalFieldSplitting
    class ElectronicGreensFunction
    class ElectronicSelfEnergy
    class Frequency
    class HoppingMatrix
    class HybridizationFunction
    class ImaginaryTime
    class MatsubaraFrequency
    class QuasiparticleWeight
    class Time
    class WignerSeitz
    BaseGreensFunction <|-- ElectronicGreensFunction
    BaseGreensFunction <|-- ElectronicSelfEnergy
    BaseGreensFunction <|-- HybridizationFunction
    BaseGreensFunction --> Frequency : real_frequency
    BaseGreensFunction --> ImaginaryTime : imaginary_time
    BaseGreensFunction --> MatsubaraFrequency : matsubara_frequency
    BaseGreensFunction --> Time : time
    BaseGreensFunction --> WignerSeitz : wigner_seitz

Legend

Parent <|-- Child inheritance (Child extends Parent)

Owner --> SubSection containment/subsection

Key sections

Section	Description	MetaInfo
BaseGreensFunction	A base class used to define shared commonalities between Green's function-related properties.	Open in MetaInfo browser
ElectronicGreensFunction	Charge-charge correlation functions.	Open in MetaInfo browser
ElectronicSelfEnergy	Corrections to the energy of an electron due to its interactions with its environment.	Open in MetaInfo browser
HybridizationFunction	Dynamical hopping of the electrons in a lattice in and out of the reservoir or bath.	Open in MetaInfo browser
QuasiparticleWeight	Renormalization of the electronic mass due to the interactions with the environment.	Open in MetaInfo browser
HoppingMatrix	Transition probability between two atomic orbitals in a tight-binding model.	Open in MetaInfo browser
CrystalFieldSplitting	Energy difference between the degenerated orbitals of an ion in a crystal field environment.	Open in MetaInfo browser

Quantities by section

BaseGreensFunction

Quantity	Type	Description
n_atoms	m_int32(int32)	Number of atoms involved in the correlations effect and used for the matrix representation of the property. Can be derived from entity_ref if needed.
entity_ref		Reference to the ElectronicState section describing the correlated orbitals for which the Green's function properties are calculated. The parent AtomsState can be accessed via entity_ref.get_parent_entity().
spin_channel	m_int32(int32)	Spin channel of the corresponding electronic property. It can take values of 0 and 1.
local_model_type	Enum	Type of Green's function calculated from the mapping of the local Hubbard-Kanamo... Type of Green's function calculated from the mapping of the local Hubbard-Kanamori model into the Anderson impurity model. The impurity Green's function describe the electronic correlations for the impurity, and it is a local function. The lattice Green's function includes the coupling to the lattice and hence it is a non-local function. In DMFT, the lattice term is approximated to be the impurity one, so that these simulations are converged if both types of the local part of the lattice Green's function coincides with the impurity Green's function.
space_id	Enum	String used to identify the space in which the Green's function property is represented. String used to identify the space in which the Green's function property is represented. The spaces are: | space_id | variable type | | ------ | ------ | | 'r' | WignerSeitz | | 'rt' | WignerSeitz + Time | | 'rw' | WignerSeitz + Frequency | | 'rit' | WignerSeitz + ImaginaryTime | | 'riw' | WignerSeitz + MatsubaraFrequency | | 'k' | KMesh | | 'kt' | KMesh + Time | | 'kw' | KMesh + Frequency | | 'kit' | KMesh + ImaginaryTime | | 'kiw' | KMesh + MatsubaraFrequency | | 't' | Time | | 'it' | Frequency | | 'w' | ImaginaryTime | | 'iw' | MatsubaraFrequency |

ElectronicGreensFunction

Quantity	Type	Description
value	m_complex128(complex128)	Value of the electronic Green's function matrix.

ElectronicSelfEnergy

Quantity	Type	Description
value	m_complex128(complex128)	Value of the electronic self-energy matrix.

HybridizationFunction

Quantity	Type	Description
value	m_complex128(complex128)	Value of the electronic hybridization function.

QuasiparticleWeight

Quantity	Type	Description
system_correlation_strengths	Enum	String used to identify the type of system based on the strength of the electron-electron interactions. String used to identify the type of system based on the strength of the electron-electron interactions. | type | Description | | ------ | ------ | | 'non-correlated metal' | All value are above 0.7. Renormalization effects are negligible. | | 'strongly-correlated metal' | All value are below 0.4 and above 0. Renormalization effects are important. | | 'OSMI' | Orbital-selective Mott insulator: some orbitals have a zero value while others a finite one. | | 'Mott insulator' | All value are 0.0. Mott insulator state. |
n_atoms	m_int32(int32)	Number of atoms involved in the correlations effect and used for the matrix representation of the quasiparticle weight. Can be derived from entity_ref if needed.
n_correlated_orbitals	m_int32(int32)	Number of orbitals involved in the correlations effect and used for the matrix representation of the quasiparticle weight.
entity_ref		Reference to the ElectronicState section describing the correlated orbitals for which the quasiparticle weight is calculated. The parent AtomsState can be accessed via entity_ref.get_parent_entity().
spin_channel	m_int32(int32)	Spin channel of the corresponding electronic property. It can take values of 0 and 1.
value	m_float_bounded(float) (shape: ['*'])	Value of the quasi-particle weight matrices. Must be between 0 and 1.

HoppingMatrix

Quantity	Type	Description
n_orbitals	m_int32(int32)	Number of orbitals in the tight-binding model. The entity_ref reference is used to refer to the ElectronicState section, which navigates to the relevant basis orbitals (e.g., SphericalSymmetryState).
degeneracy_factors	m_int32(int32) (shape: ['*'])	Degeneracy of each Wigner-Seitz point.
value	m_complex128(complex128)	Value of the hopping matrix in joules. The elements are complex numbers defined for each Wigner-Seitz point and each pair of orbitals. Note this contains also the onsite values, i.e., it includes the Wigner-Seitz point (0, 0, 0), hence the CrystalFieldSplitting values.

CrystalFieldSplitting

Quantity	Type	Description
n_orbitals	m_int32(int32)	Number of orbitals in the tight-binding model. The entity_ref reference is used to refer to the ElectronicState section, which navigates to the relevant basis orbitals (e.g., SphericalSymmetryState).
value	m_float64(float64)	Value of the crystal field splittings in joules. This is the intra-orbital local contribution, i.e., the same orbital at the same Wigner-Seitz point (0, 0, 0).