Pomerol::GreensFunctionPart Class Reference

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

#include <GreensFunctionPart.hpp>

Inheritance diagram for Pomerol::GreensFunctionPart:

Collaboration diagram for Pomerol::GreensFunctionPart:

Public Member Functions
	GreensFunctionPart (MonomialOperatorPart const &C, MonomialOperatorPart const &CX, HamiltonianPart const &HpartInner, HamiltonianPart const &HpartOuter, DensityMatrixPart const &DMpartInner, DensityMatrixPart const &DMpartOuter)
void	compute ()
	Compute the terms contributing to this part. More...
ComplexType	operator() (ComplexType z) const
ComplexType	operator() (long MatsubaraNumber) const
ComplexType	of_tau (RealType tau) const
Public Member Functions inherited from Pomerol::Thermal
	Thermal (RealType beta)

Friends
std::ostream &	operator<< (std::ostream &os, Term const &T)

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 single-particle Matsubara Green's function.

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

\[ \langle {\rm outer} | c | {\rm inner} \rangle\langle {\rm inner} | c^\dagger | {\rm outer} \rangle \]

with (inner, outer) being a certain pair of Hamiltonian's invariant subspaces. The contributions are stored as terms of the Lehmann representation, i.e. as fractions \(\frac{R}{z - P}\) with real poles \(P\) and complex residues \(R\). The latter are combinations of matrix elements and statistical weights.

Definition at line 48 of file GreensFunctionPart.hpp.

Constructor & Destructor Documentation

GreensFunctionPart()

Pomerol::GreensFunctionPart::GreensFunctionPart	(	MonomialOperatorPart const &	C,
		MonomialOperatorPart const &	CX,
		HamiltonianPart const &	HpartInner,
		HamiltonianPart const &	HpartOuter,
		DensityMatrixPart const &	DMpartInner,
		DensityMatrixPart const &	DMpartOuter
	)

Constructor.

Parameters

[in]	C	Part of the annihilation operator \(c\).
[in]	CX	Part of the creation operator \(c^\dagger\).
[in]	HpartInner	Part of the Hamiltonian corresponding to the 'inner' subspace.
[in]	HpartOuter	Part of the Hamiltonian corresponding to the 'outer' subspace.
[in]	DMpartInner	Part of the many-body density matrix \(\hat\rho\) corresponding to the 'inner' subspace.
[in]	DMpartOuter	Part of the many-body density matrix \(\hat\rho\) corresponding to the 'outer' subspace.

Member Function Documentation

compute()

void Pomerol::GreensFunctionPart::compute

(

)

Compute the terms contributing to this part.

of_tau()

ComplexType Pomerol::GreensFunctionPart::of_tau ( RealType  tau ) const

inline

Return the contribution to the imaginary-time Green's function made by this part.

Parameters

[in]

tau

Imaginary time point.

Definition at line 208 of file GreensFunctionPart.hpp.

operator()() [1/2]

ComplexType Pomerol::GreensFunctionPart::operator() ( ComplexType  z ) const

inline

Substitute a complex frequency \(z\) into this part.

Parameters

[in]

z

Value of the frequency \(z\).

Definition at line 204 of file GreensFunctionPart.hpp.

operator()() [2/2]

ComplexType Pomerol::GreensFunctionPart::operator() ( long  MatsubaraNumber ) const

inline

Substitute a fermionic Matsubara frequency \(\omega_n\) into this part.

Parameters

[in]

MatsubaraNumber

Index of the Matsubara frequency \(n\) ( \( \omega_n = \pi (2n + 1)/\beta \)).

Definition at line 200 of file GreensFunctionPart.hpp.

Friends And Related Function Documentation

operator<<

std::ostream& operator<< ( std::ostream &  os, Term const &  T  )

friend

Output stream insertion operator.

Parameters

[out]	os	Output stream.
[in]	T	Term to be inserted.

Returns

Reference to the output stream.

Definition at line 149 of file GreensFunctionPart.hpp.

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

• pomerol/GreensFunctionPart.hpp