Pomerol::Susceptibility Class Reference

Dynamical susceptibility. More...

#include <Susceptibility.hpp>

Inheritance diagram for Pomerol::Susceptibility:

Collaboration diagram for Pomerol::Susceptibility:

Public Member Functions
	Susceptibility (StatesClassification const &S, Hamiltonian const &H, MonomialOperator const &A, MonomialOperator const &B, DensityMatrix const &DM)
	Susceptibility (Susceptibility const &Chi)
void	prepare ()
void	compute ()
	Actually computes the parts. More...
void	subtractDisconnected ()
void	subtractDisconnected (ComplexType ave_A, ComplexType ave_B)
void	subtractDisconnected (EnsembleAverage &EA_A, EnsembleAverage &EA_B)
ComplexType	operator() (long MatsubaraNumber) const
ComplexType	operator() (ComplexType z) const
ComplexType	of_tau (RealType tau) const
bool	isVanishing () const
	Is this susceptibility 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

Dynamical susceptibility.

This class represents a dynamical susceptibility in the Matsubara space,

\[ \chi(i\omega_n) = \int_0^\beta Tr[\mathcal{T}_\tau \hat\rho A(\tau) B(0)] e^{i\omega_n\tau} d\tau \]

and its connected part,

\[ \tilde{\chi}(i\omega_n) = \chi(i\omega_n) - \beta \langle\hat A \rangle \langle\hat B \rangle. \]

Here, \(\beta\) is inverse temperature and \(\langle\hat A\rangle, \langle\hat B\rangle\) are EnsembleAverage's of boson-like monomial operators \(\hat A, \hat B\).

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

Definition at line 54 of file Susceptibility.hpp.

Constructor & Destructor Documentation

Susceptibility() [1/2]

Pomerol::Susceptibility::Susceptibility	(	StatesClassification const &	S,
		Hamiltonian const &	H,
		MonomialOperator const &	A,
		MonomialOperator const &	B,
		DensityMatrix const &	DM
	)

Constructor.

Parameters

[in]	S	Information about invariant subspaces of the Hamiltonian.
[in]	H	The Hamiltonian.
[in]	A	Monomial operator \(\hat A\).
[in]	B	Monomial operator \(\hat B\).
[in]	DM	Many-body density matrix \(\hat\rho\).

Susceptibility() [2/2]

Pomerol::Susceptibility::Susceptibility

(

Susceptibility const &

Chi

)

Copy-constructor.

Parameters

[in]

Chi

Susceptibility object to be copied.

Member Function Documentation

compute()

void Pomerol::Susceptibility::compute

(

)

Actually computes the parts.

isVanishing()

bool Pomerol::Susceptibility::isVanishing ( ) const

inline

Is this susceptibility identically zero?

Definition at line 132 of file Susceptibility.hpp.

of_tau()

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

inline

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

Parameters

[in]

tau

Imaginary time point.

Definition at line 154 of file Susceptibility.hpp.

operator()() [1/2]

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

inline

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

Parameters

[in]

z

The complex frequency.

Definition at line 141 of file Susceptibility.hpp.

operator()() [2/2]

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

inline

Return the susceptibility value calculated at a given Matsubara frequency.

Parameters

[in]

MatsubaraNumber

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

Definition at line 137 of file Susceptibility.hpp.

prepare()

void Pomerol::Susceptibility::prepare

(

)

Select all relevant parts of \(\hat A\) and \(\hat B\) and allocate resources for the SusceptibilityPart's.

subtractDisconnected() [1/3]

void Pomerol::Susceptibility::subtractDisconnected

(

)

Activate subtraction of the disconnected part \(\langle\hat A \rangle \langle\hat B \rangle\). \(\langle\hat A \rangle\) and \(\langle\hat B \rangle\) are computed by this class.

subtractDisconnected() [2/3]

void Pomerol::Susceptibility::subtractDisconnected	(	ComplexType	ave_A,
		ComplexType	ave_B
	)

Activate subtraction of the disconnected part \(\langle\hat A \rangle \langle\hat B \rangle\). Precomputed ensemble averages must be provided by the caller.

Parameters

[in]	ave_A	Precomputed value of \(\langle\hat A \rangle\).
[in]	ave_B	Precomputed value of \(\langle\hat B \rangle\).

subtractDisconnected() [3/3]

void Pomerol::Susceptibility::subtractDisconnected	(	EnsembleAverage &	EA_A,
		EnsembleAverage &	EA_B
	)

Activate subtraction of the disconnected part \(\langle\hat A \rangle \langle\hat B \rangle\). EnsembleAverage objects must must be provided by the caller.

Parameters

[in]	EA_A	Predefined EnsembleAverage class for the operator \(\hat A\).
[in]	EA_B	Predefined EnsembleAverage class for the operator \(\hat B\).

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

• pomerol/Susceptibility.hpp