Fermionic two-particle Matsubara Green's function. More...

#include <TwoParticleGF.hpp>

Inheritance diagram for Pomerol::TwoParticleGF:

Collaboration diagram for Pomerol::TwoParticleGF:

Public Member Functions
	TwoParticleGF (StatesClassification const &S, Hamiltonian const &H, AnnihilationOperator const &C1, AnnihilationOperator const &C2, CreationOperator const &CX3, CreationOperator const &CX4, DensityMatrix const &DM)

void	prepare ()
	Choose relevant parts of \(c_i,c_j,c^\dagger_k,c^\dagger_l\) and allocate resources for the parts. More...

std::vector< ComplexType >	compute (bool clear=false, FreqVec3 const &freqs={}, MPI_Comm const &comm=MPI_COMM_WORLD)

ParticleIndex	getIndex (std::size_t Position) const

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

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

bool	isVanishing () const
	Is this Green's function identically zero? More...

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)

Data Fields
RealType	ReduceResonanceTolerance = 1e-8
	A difference in energies with magnitude below this value is treated as zero. More...

RealType	CoefficientTolerance = 1e-16
	Minimal magnitude of the coefficient of a term for it to be taken into account. More...

RealType	MultiTermCoefficientTolerance = 1e-5

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 Member Functions
MonomialOperatorPart const &	OperatorPartAtPosition (std::size_t PermutationNumber, std::size_t OperatorPosition, BlockNumber LeftIndex) const

BlockNumber	getLeftIndex (std::size_t PermutationNumber, std::size_t OperatorPosition, BlockNumber RightIndex) const

BlockNumber	getRightIndex (std::size_t PermutationNumber, std::size_t OperatorPosition, BlockNumber LeftIndex) const

Protected Attributes
bool	Vanishing = true
	A flag that marks an identically vanishing Green's function. More...

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

Friends
class	TwoParticleGFContainer

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

Detailed Description

Fermionic two-particle Matsubara Green's function.

\[ \chi_{ijkl}(\omega_{n_1},\omega_{n_2};\omega_{n_3},\omega_{n_1}+\omega_{n_2}-\omega_{n_3}) = \int_0^\beta Tr[\mathcal{T}_\tau \hat\rho c_i(\tau_1)c_j(\tau_2)c^\dagger_k(\tau_3)c^\dagger_l(0)] e^{i\omega_{n_1}\tau_1+i\omega_{n_2}\tau_2-i\omega_{n_3}\tau_3} d\tau_1 d\tau_2 d\tau_3. \]

It is actually a container class for a collection of TwoParticleGFPart's (most of the real calculations take place in the parts).

Definition at line 60 of file TwoParticleGF.hpp.

Constructor & Destructor Documentation

◆ TwoParticleGF()

Pomerol::TwoParticleGF::TwoParticleGF	(	StatesClassification const &	S,
		Hamiltonian const &	H,
		AnnihilationOperator const &	C1,
		AnnihilationOperator const &	C2,
		CreationOperator const &	CX3,
		CreationOperator const &	CX4,
		DensityMatrix const &	DM
	)

Constructor.

Parameters

[in]	S	Information about invariant subspaces of the Hamiltonian.
[in]	H	The Hamiltonian.
[in]	C1	The annihilation operator \(c_i\).
[in]	C2	The annihilation operator \(c_j\).
[in]	CX3	The creation operator \(c^\dagger_k\).
[in]	CX4	The creation operator \(c^\dagger_l\).
[in]	DM	Many-body density matrix \(\hat\rho\).

Member Function Documentation

◆ compute()

std::vector<ComplexType> Pomerol::TwoParticleGF::compute	(	bool	clear = `false`,
		FreqVec3 const &	freqs = `{}`,
		MPI_Comm const &	comm = `MPI_COMM_WORLD`
	)

Compute the parts in parallel and fill the internal cache of precomputed values.

Parameters

[in]	clear	If true, computed TwoParticleGFPart's will be destroyed immediately after filling the precomputed value cache.
[in]	freqs	List of frequency triplets \((\omega_{n_1},\omega_{n_2},\omega_{n_3})\).
[in]	comm	MPI communicator used to parallelize the computation.

Returns: A list of precomputed values.

Precondition: prepare() has been called.

◆ getIndex()

ParticleIndex Pomerol::TwoParticleGF::getIndex ( std::size_t Position ) const

Returns the single particle index of one of the operators \(c_i,c_j,c^\dagger_k,c^\dagger_l\).

Parameters

[in] Position Position of the requested operator, 0–3.

◆ getLeftIndex()

BlockNumber Pomerol::TwoParticleGF::getLeftIndex	(	std::size_t	PermutationNumber,
		std::size_t	OperatorPosition,
		BlockNumber	RightIndex
	)		const

protected

Choose the operator standing at a specified position in a given permutation of the list \(\{c_i,c_j,c^\dagger_k,c^\dagger_l\}\) and return its left invariant subspace index corresponding to a given right subspace index. Return INVALID_BLOCK_NUMBER if the operator does not have such a (non-zero) block.

Parameters

[in]	PermutationNumber	Serial number of the permutation within permutations3.
[in]	OperatorPosition	Position of the operator, 0–3.
[in]	RightIndex	The right invariant subspace index.

◆ getRightIndex()

BlockNumber Pomerol::TwoParticleGF::getRightIndex	(	std::size_t	PermutationNumber,
		std::size_t	OperatorPosition,
		BlockNumber	LeftIndex
	)		const

protected

Choose the operator standing at a specified position in a given permutation of the list \(\{c_i,c_j,c^\dagger_k,c^\dagger_l\}\) and return its right invariant subspace index corresponding to a given left subspace index. Return INVALID_BLOCK_NUMBER if the operator does not have such a (non-zero) block.

Parameters

[in]	PermutationNumber	Serial number of the permutation within permutations3.
[in]	OperatorPosition	Position of the operator, 0–3.
[in]	LeftIndex	The left invariant subspace index.

◆ isVanishing()

bool Pomerol::TwoParticleGF::isVanishing ( ) const

inline

Is this Green's function identically zero?

Definition at line 169 of file TwoParticleGF.hpp.

◆ operator()() [1/2]

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

inline

Return the value of the two-particle Green's function calculated at a given complex frequency triplet. This method ignores the precomputed value cache.

Parameters

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

Definition at line 174 of file TwoParticleGF.hpp.

◆ operator()() [2/2]

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

inline

Return the value of the two-particle Green's function 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 \(n_3\) ( \(\omega_{n_3}=\pi(2n_3+1)/\beta\)).

Definition at line 186 of file TwoParticleGF.hpp.

◆ OperatorPartAtPosition()

MonomialOperatorPart const& Pomerol::TwoParticleGF::OperatorPartAtPosition	(	std::size_t	PermutationNumber,
		std::size_t	OperatorPosition,
		BlockNumber	LeftIndex
	)		const

protected

Extract the operator part standing at a specified position in a given permutation of the list \(\{c_i,c_j,c^\dagger_k,c^\dagger_l\}\).

Parameters

[in]	PermutationNumber	Serial number of the permutation within permutations3.
[in]	OperatorPosition	Position of the operator, 0–3.
[in]	LeftIndex	The left invariant subspace index referring to the requested part.

◆ prepare()

void Pomerol::TwoParticleGF::prepare ( )

Choose relevant parts of \(c_i,c_j,c^\dagger_k,c^\dagger_l\) and allocate resources for the parts.

Friends And Related Function Documentation

◆ TwoParticleGFContainer

friend class TwoParticleGFContainer

friend

Definition at line 62 of file TwoParticleGF.hpp.

Field Documentation

◆ CoefficientTolerance

RealType Pomerol::TwoParticleGF::CoefficientTolerance = 1e-16

Minimal magnitude of the coefficient of a term for it to be taken into account.

Definition at line 115 of file TwoParticleGF.hpp.

◆ MultiTermCoefficientTolerance

RealType Pomerol::TwoParticleGF::MultiTermCoefficientTolerance = 1e-5

Minimal magnitude of the coefficient of a term for it to be taken into account with respect to the amount of terms.

Definition at line 118 of file TwoParticleGF.hpp.

◆ ReduceResonanceTolerance

RealType Pomerol::TwoParticleGF::ReduceResonanceTolerance = 1e-8

A difference in energies with magnitude below this value is treated as zero.

Definition at line 113 of file TwoParticleGF.hpp.

◆ Vanishing

bool Pomerol::TwoParticleGF::Vanishing = true

protected

A flag that marks an identically vanishing Green's function.

Definition at line 84 of file TwoParticleGF.hpp.

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

pomerol/TwoParticleGF.hpp

Public Member Functions

Data Fields

Protected Member Functions

Protected Attributes

Friends

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ TwoParticleGF()

Member Function Documentation

◆ compute()

◆ getIndex()

◆ getLeftIndex()

◆ getRightIndex()

◆ isVanishing()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ OperatorPartAtPosition()

◆ prepare()

Friends And Related Function Documentation

◆ TwoParticleGFContainer

Field Documentation

◆ CoefficientTolerance

◆ MultiTermCoefficientTolerance

◆ ReduceResonanceTolerance

◆ Vanishing