Part of a fermionic two-particle Matsubara Green's function. More...

#include <TwoParticleGFPart.hpp>

Inheritance diagram for Pomerol::TwoParticleGFPart:

Collaboration diagram for Pomerol::TwoParticleGFPart:

Data Structures
struct	NonResonantTerm
	A non-resonant term in the Lehmann representation of TwoParticleGF. More...

struct	ResonantTerm
	A resonant term in the Lehmann representation of TwoParticleGF. More...

Public Member Functions
	TwoParticleGFPart (MonomialOperatorPart const &O1, MonomialOperatorPart const &O2, MonomialOperatorPart const &O3, MonomialOperatorPart const &CX4, HamiltonianPart const &Hpart1, HamiltonianPart const &Hpart2, HamiltonianPart const &Hpart3, HamiltonianPart const &Hpart4, DensityMatrixPart const &DMpart1, DensityMatrixPart const &DMpart2, DensityMatrixPart const &DMpart3, DensityMatrixPart const &DMpart4, Permutation3 Permutation)

void	compute ()
	Compute the terms contributing to this part. More...

void	clear ()
	Purge all terms. More...

ComplexType	operator() (ComplexType z1, ComplexType z2, ComplexType z3) const

ComplexType	operator() (long MatsubaraNumber1, long MatsubaraNumber2, long MatsubaraNumber3) const

std::size_t	getNumResonantTerms () const
	Return the number of resonant terms. More...

std::size_t	getNumNonResonantTerms () const
	Return the number of non-resonant terms. More...

Permutation3 const &	getPermutation () const
	Return the permutation of operators \(\{c_i, c_j, c^\dagger_k\}\) for this part. More...

TermList< TwoParticleGFPart::ResonantTerm > const &	getResonantTerms () const
	Access the list of the resonant terms. More...

TermList< TwoParticleGFPart::NonResonantTerm > const &	getNonResonantTerms () const
	Access the list of the non-resonant terms. More...

Public Member Functions inherited from Pomerol::Thermal
	Thermal (RealType beta)

Friends
class	TwoParticleGF

class	TwoParticleGFContainer

Additional Inherited Members
Data Fields inherited from Pomerol::Thermal
const RealType	beta
	Inverse temperature \(\beta\). More...

const ComplexType	MatsubaraSpacing
	Spacing between (imaginary) Matsubara frequencies, \(i\pi/\beta\). More...

Detailed Description

Part of a fermionic two-particle Matsubara Green's function.

It includes contributions from all matrix elements of the following form,

\[ \langle {\rm S_1}| \hat O_1 |{\rm S_2}\rangle \langle {\rm S_2}| \hat O_2 |{\rm S_3} \rangle \langle {\rm S_3}| \hat O_3 |{\rm S_4} \rangle \langle {\rm S_4}| c^\dagger_l |{\rm S_1} \rangle, \]

where \(\{\hat O_1, \hat O_2, \hat O_3\}\) is a permutation of operators \(\{c_i, c_j, c^\dagger_k\}\) and \({\rm S_1}, {\rm S_2}, {\rm S_3}, {\rm S_4}\) are invariant subspaces of the Hamiltonian. The contributions are stored as terms of the Lehmann representation. There are two kinds of terms contributing to the expansion, so called resonant (ResonantTerm) and non-resonant (NonResonantTerm) terms.

Definition at line 54 of file TwoParticleGFPart.hpp.

Constructor & Destructor Documentation

◆ TwoParticleGFPart()

Pomerol::TwoParticleGFPart::TwoParticleGFPart	(	MonomialOperatorPart const &	O1,
		MonomialOperatorPart const &	O2,
		MonomialOperatorPart const &	O3,
		MonomialOperatorPart const &	CX4,
		HamiltonianPart const &	Hpart1,
		HamiltonianPart const &	Hpart2,
		HamiltonianPart const &	Hpart3,
		HamiltonianPart const &	Hpart4,
		DensityMatrixPart const &	DMpart1,
		DensityMatrixPart const &	DMpart2,
		DensityMatrixPart const &	DMpart3,
		DensityMatrixPart const &	DMpart4,
		Permutation3	Permutation
	)

Constructor.

Parameters

[in]	O1	Part of the field operator \(\hat O_1\).
[in]	O2	Part of the field operator \(\hat O_2\).
[in]	O3	Part of the field operator \(\hat O_3\).
[in]	CX4	Part of the creation operator \(\hat c^\dagger_l\).
[in]	Hpart1	Part of the Hamiltonian corresponding to the subspace \({\rm S_1}\).
[in]	Hpart2	Part of the Hamiltonian corresponding to the subspace \({\rm S_2}\).
[in]	Hpart3	Part of the Hamiltonian corresponding to the subspace \({\rm S_3}\).
[in]	Hpart4	Part of the Hamiltonian corresponding to the subspace \({\rm S_4}\).
[in]	DMpart1	Part of the many-body density matrix corresponding to the subspace \({\rm S_1}\).
[in]	DMpart2	Part of the many-body density matrix corresponding to the subspace \({\rm S_2}\).
[in]	DMpart3	Part of the many-body density matrix corresponding to the subspace \({\rm S_3}\).
[in]	DMpart4	Part of the many-body density matrix corresponding to the subspace \({\rm S_4}\).
[in]	Permutation	Permutation of operators \(\{c_i, c_j, c^\dagger_k\}\) for this part.

Member Function Documentation

◆ clear()

void Pomerol::TwoParticleGFPart::clear ( )

Purge all terms.

◆ compute()

void Pomerol::TwoParticleGFPart::compute ( )

Compute the terms contributing to this part.

◆ getNonResonantTerms()

TermList<TwoParticleGFPart::NonResonantTerm> const& Pomerol::TwoParticleGFPart::getNonResonantTerms ( ) const

inline

Access the list of the non-resonant terms.

Definition at line 467 of file TwoParticleGFPart.hpp.

◆ getNumNonResonantTerms()

std::size_t Pomerol::TwoParticleGFPart::getNumNonResonantTerms ( ) const

inline

Return the number of non-resonant terms.

Definition at line 459 of file TwoParticleGFPart.hpp.

◆ getNumResonantTerms()

std::size_t Pomerol::TwoParticleGFPart::getNumResonantTerms ( ) const

inline

Return the number of resonant terms.

Definition at line 457 of file TwoParticleGFPart.hpp.

◆ getPermutation()

Permutation3 const& Pomerol::TwoParticleGFPart::getPermutation ( ) const

inline

Return the permutation of operators \(\{c_i, c_j, c^\dagger_k\}\) for this part.

Definition at line 462 of file TwoParticleGFPart.hpp.

◆ getResonantTerms()

TermList<TwoParticleGFPart::ResonantTerm> const& Pomerol::TwoParticleGFPart::getResonantTerms ( ) const

inline

Access the list of the resonant terms.

Definition at line 465 of file TwoParticleGFPart.hpp.

◆ operator()() [1/2]

ComplexType Pomerol::TwoParticleGFPart::operator()	(	ComplexType	z1,
		ComplexType	z2,
		ComplexType	z3
	)		const

Substitute complex frequencies \(z_1, z_2, z_3\) into this part.

Parameters

[in]	z1	First frequency \(z_1\).
[in]	z2	Second frequency \(z_2\).
[in]	z3	Third frequency \(z_3\).

◆ operator()() [2/2]

ComplexType Pomerol::TwoParticleGFPart::operator()	(	long	MatsubaraNumber1,
		long	MatsubaraNumber2,
		long	MatsubaraNumber3
	)		const

Substitute Matsubara frequencies \(i\omega_{n_1}, i\omega_{n_2}, i\omega_{n_3}\) into this part.

Parameters

[in]	MatsubaraNumber1	Index of the first Matsubara frequency \(n_1\) ( \(\omega_{n_1}=\pi(2n_1+1)/\beta\)).
[in]	MatsubaraNumber2	Index of the second Matsubara frequency \(n_2\) ( \(\omega_{n_2}=\pi(2n_2+1)/\beta\)).
[in]	MatsubaraNumber3	Index of the third Matsubara frequency \(n_3\) ( \(\omega_{n_3}=\pi(2n_3+1)/\beta\)).

Friends And Related Function Documentation

◆ TwoParticleGF

friend class TwoParticleGF

friend

Definition at line 56 of file TwoParticleGFPart.hpp.

◆ TwoParticleGFContainer

friend class TwoParticleGFContainer

friend

Definition at line 57 of file TwoParticleGFPart.hpp.

The documentation for this class was generated from the following file:

pomerol/TwoParticleGFPart.hpp

Data Structures

Public Member Functions

Friends

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ TwoParticleGFPart()

Member Function Documentation

◆ clear()

◆ compute()

◆ getNonResonantTerms()

◆ getNumNonResonantTerms()

◆ getNumResonantTerms()

◆ getPermutation()

◆ getResonantTerms()

◆ operator()() [1/2]

◆ operator()() [2/2]

Friends And Related Function Documentation

◆ TwoParticleGF

◆ TwoParticleGFContainer