Pomerol::DensityMatrixPart Class Reference

Part of a many-body Gibbs density matrix. More...

#include <DensityMatrixPart.hpp>

Inheritance diagram for Pomerol::DensityMatrixPart:

Collaboration diagram for Pomerol::DensityMatrixPart:

Public Member Functions
	DensityMatrixPart (HamiltonianPart const &H, RealType beta, RealType GroundEnergy)
RealType	computeUnnormalized ()
	Compute and store the unnormalized statistical weights \(Z w_s\). More...
void	normalize (RealType Z)
RealType	getWeight (InnerQuantumState s) const
RealType	getAverageEnergy () const
	Compute the energy averaged over this block, \( \langle E\rangle = \sum_{s\in B} E_s w_s\). More...
RealType	getPartialZ () const
	Return the contribution of this block to the partition function, \(Z_B = Z\sum_{s\in B} w_s\). More...
void	truncate (RealType Tolerance)
bool	isRetained () const
	Does this block contain any non-negligible statistical weights? More...
Public Member Functions inherited from Pomerol::Thermal
	Thermal (RealType beta)

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 many-body Gibbs density matrix.

This class represents a part (diagonal block \(B\)) of a many-body Gibbs density matrix

\[ \hat\rho = \frac{e^{-\beta\hat H}}{Z}, \quad Z = Tr[e^{-\beta\hat H}]. \]

Since the matrix is always computed in the eigenbasis of \(\hat H\), it is sufficient to store its eigenvalues (statistical weights \(w_s = e^{-\beta E_s} / Z\)).

Definition at line 39 of file DensityMatrixPart.hpp.

Constructor & Destructor Documentation

DensityMatrixPart()

Pomerol::DensityMatrixPart::DensityMatrixPart	(	HamiltonianPart const &	H,
		RealType	beta,
		RealType	GroundEnergy
	)

Constructor.

Parameters

[in]	H	The respective diagonal block of the Hamiltonian.
[in]	beta	Inverse temperature \(\beta\).
[in]	GroundEnergy	The ground state energy of the Hamiltonian.

Member Function Documentation

computeUnnormalized()

RealType Pomerol::DensityMatrixPart::computeUnnormalized

(

)

Compute and store the unnormalized statistical weights \(Z w_s\).

getAverageEnergy()

RealType Pomerol::DensityMatrixPart::getAverageEnergy

(

)

const

Compute the energy averaged over this block, \( \langle E\rangle = \sum_{s\in B} E_s w_s\).

getPartialZ()

RealType Pomerol::DensityMatrixPart::getPartialZ ( ) const

inline

Return the contribution of this block to the partition function, \(Z_B = Z\sum_{s\in B} w_s\).

Definition at line 81 of file DensityMatrixPart.hpp.

getWeight()

RealType Pomerol::DensityMatrixPart::getWeight

(

InnerQuantumState

s

)

const

Return a statistical weight \(w_s\).

Parameters

[in]

s

Index of the weight within this block.

isRetained()

bool Pomerol::DensityMatrixPart::isRetained ( ) const

inline

Does this block contain any non-negligible statistical weights?

Definition at line 89 of file DensityMatrixPart.hpp.

normalize()

void Pomerol::DensityMatrixPart::normalize

(

RealType

Z

)

Normalize the stored statistical weights by the partition function \(Z\).

Parameters

[in]

Z

The partition function.

truncate()

void Pomerol::DensityMatrixPart::truncate

(

RealType

Tolerance

)

Check if any of the statistical weights is above a given tolerance. If not, mark this block as irrelevant (set the Retained flag to false).

Parameters

[in]

Tolerance

Statistical weights smaller or equal to this value are considered negligible.

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

• pomerol/DensityMatrixPart.hpp