Irreducible two-particle vertex. More...

#include <Vertex4.hpp>

Inheritance diagram for Pomerol::Vertex4:

Collaboration diagram for Pomerol::Vertex4:

Public Member Functions
	Vertex4 (TwoParticleGF const &Chi, GreensFunction const &G13, GreensFunction const &G24, GreensFunction const &G14, GreensFunction const &G23)

void	compute (long NumberOfMatsubaras=0)

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

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

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

Public Member Functions inherited from Pomerol::ComputableObject
	ComputableObject ()=default

StatusEnum	getStatus () const
	Return the current computation status. More...

void	setStatus (StatusEnum Status_in)

Friends
class	MatsubaraContainer4< Vertex4 >

Additional Inherited Members
Public Types inherited from Pomerol::ComputableObject
enum	StatusEnum { Constructed, Prepared, Computed }
	Computation status of the object. More...

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...

Protected Attributes inherited from Pomerol::ComputableObject
StatusEnum	Status = Constructed
	Current computation status. More...

Detailed Description

Irreducible two-particle vertex.

Irreducible two-particle vertex part of fermions,

\[ \Gamma_{ijkl}(\omega_{n_1},\omega_{n_2};\omega_{n_3},\omega_{n_4}) = \chi_{ijkl}(\omega_{n_1},\omega_{n_2};\omega_{n_3},\omega_{n_4}) - \chi^0_{ijkl}(\omega_{n_1},\omega_{n_2};\omega_{n_3},\omega_{n_4}) \]

with the Wick part of the two-particle Green's function being

\[ \chi^0_{ijkl}(\omega_{n_1},\omega_{n_2};\omega_{n_3},\omega_{n_4}) = \beta\delta_{\omega_{n_1}\omega_{n_4}}\delta_{\omega_{n_2}\omega_{n_3}}G_{il}(\omega_{n_1})G_{jk}(\omega_{n_2}) - \beta\delta_{\omega_{n_1}\omega_{n_3}}\delta_{\omega_{n_2}\omega_{n_4}}G_{ik}(\omega_{n_1})G_{jl}(\omega_{n_2}). \]

\(\beta\) is the inverse temperature, \(G_{ij}\) is the single-particle Green's function, and \(\omega_{n_4} = \omega_{n_1}+\omega_{n_2}-\omega_{n_3}\).

Definition at line 47 of file Vertex4.hpp.

Constructor & Destructor Documentation

◆ Vertex4()

Pomerol::Vertex4::Vertex4	(	TwoParticleGF const &	Chi,
		GreensFunction const &	G13,
		GreensFunction const &	G24,
		GreensFunction const &	G14,
		GreensFunction const &	G23
	)

Constructor.

Parameters

[in]	Chi	Fermionic two-particle Matsubara Green's function \(\chi_{ijkl}\)
[in]	G13	Fermionic single-particle Matsubara Green's function \(G_{ik}\).
[in]	G24	Fermionic single-particle Matsubara Green's function \(G_{jl}\).
[in]	G14	Fermionic single-particle Matsubara Green's function \(G_{il}\).
[in]	G23	Fermionic single-particle Matsubara Green's function \(G_{jk}\).

Member Function Documentation

◆ compute()

void Pomerol::Vertex4::compute ( long NumberOfMatsubaras = 0 )

Populate the internal cache of precomputed values.

Parameters

[in] NumberOfMatsubaras Number of positive fermionic Matsubara frequencies \(\omega_{n_1}\) and \(\omega_{n_2}\) for which values are precomputed and stored.

◆ operator()()

ComplexType Pomerol::Vertex4::operator()	(	long	MatsubaraNumber1,
		long	MatsubaraNumber2,
		long	MatsubaraNumber3
	)		const

Return the value of the vertex calculated a given Matsubara frequency triplet.

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 \(n_3\) ( \(\omega_{n_3}=\pi(2n_3+1)/\beta\)).

◆ value()

ComplexType Pomerol::Vertex4::value	(	long	MatsubaraNumber1,
		long	MatsubaraNumber2,
		long	MatsubaraNumber3
	)		const

Return the value of vertex calculated a given Matsubara frequency triplet. This method ignores the internal cache of precomputed values.

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 \(n_3\) ( \(\omega_{n_3}=\pi(2n_3+1)/\beta\)).