Pomerol::GreensFunction Class Reference

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

#include <GreensFunction.hpp>

Inheritance diagram for Pomerol::GreensFunction:

Collaboration diagram for Pomerol::GreensFunction:

Public Member Functions
	GreensFunction (StatesClassification const &S, Hamiltonian const &H, AnnihilationOperator const &C, CreationOperator const &CX, DensityMatrix const &DM)
	GreensFunction (GreensFunction const &GF)
void	prepare ()
void	compute ()
	Actually computes the parts. More...
ParticleIndex	getIndex (std::size_t Position) const
ComplexType	operator() (long MatsubaraNumber) const
ComplexType	operator() (ComplexType z) const
ComplexType	of_tau (RealType tau) 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)

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

Fermionic single-particle Matsubara Green's function.

This class gives access to the GF values both in imaginary time representation,

\[ G(\tau) = -Tr[\mathcal{T}_\tau \hat\rho c(\tau) c^\dagger(0)] \]

and at the imaginary Matsubara frequencies \(\omega_n = \pi(2n+1)/\beta\),

\[ G(i\omega_n) = \int_0^\beta d\tau e^{i\omega_n\tau} G(\tau). \]

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

Definition at line 48 of file GreensFunction.hpp.

Constructor & Destructor Documentation

GreensFunction() [1/2]

Pomerol::GreensFunction::GreensFunction	(	StatesClassification const &	S,
		Hamiltonian const &	H,
		AnnihilationOperator const &	C,
		CreationOperator const &	CX,
		DensityMatrix const &	DM
	)

Constructor.

Parameters

[in]	S	Information about invariant subspaces of the Hamiltonian.
[in]	H	The Hamiltonian.
[in]	C	The annihilation operator \(c\).
[in]	CX	The creation operator \(c^\dagger\).
[in]	DM	Many-body density matrix \(\hat\rho\).

GreensFunction() [2/2]

Pomerol::GreensFunction::GreensFunction

(

GreensFunction const &

GF

)

Copy-constructor.

Parameters

[in]

GF

GreensFunction object to be copied.

Member Function Documentation

compute()

void Pomerol::GreensFunction::compute

(

)

Actually computes the parts.

getIndex()

ParticleIndex Pomerol::GreensFunction::getIndex

(

std::size_t

Position

)

const

Returns the single-particle index of either \(c\) or \(c^\dagger\).

Parameters

[in]

Position

Select \(c\) for Position==0 and \(c^\dagger\) for Position==1. Throws for other values of this argument.

isVanishing()

bool Pomerol::GreensFunction::isVanishing ( ) const

inline

Is this Green's function identically zero?

Definition at line 109 of file GreensFunction.hpp.

of_tau()

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

inline

Return the GF value calculated at a given imaginary time \(\tau\).

Parameters

[in]

tau

Imaginary time point.

Definition at line 129 of file GreensFunction.hpp.

operator()() [1/2]

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

inline

Return the GF value calculated at a given complex frequency \(z\).

Parameters

[in]

z

The complex frequency.

Definition at line 118 of file GreensFunction.hpp.

operator()() [2/2]

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

inline

Return the GF value calculated at a given Matsubara frequency.

Parameters

[in]

MatsubaraNumber

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

Definition at line 114 of file GreensFunction.hpp.

prepare()

void Pomerol::GreensFunction::prepare

(

)

Select all relevant parts of \(c\) and \(c^\dagger\) and allocate resources for the GreensFunctionPart's.

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

• pomerol/GreensFunction.hpp