#include <TwoDM.h>

Public Member Functions
	TwoDM (const SyBookkeeper denBKIn, const Problem ProbIn)
	Constructor. More...

virtual	~TwoDM ()
	Destructor.

double	getTwoDMA_DMRG (const int cnt1, const int cnt2, const int cnt3, const int cnt4) const
	Get a 2DM_A term, using the DMRG indices. More...

double	getTwoDMB_DMRG (const int cnt1, const int cnt2, const int cnt3, const int cnt4) const
	Get a 2DM_B term, using the DMRG indices. More...

double	get1RDM_DMRG (const int cnt1, const int cnt2) const
	Get a 1-RDM term, using the DMRG indices. More...

double	spin_density_dmrg (const int cnt1, const int cnt2) const
	Get a spin-density term, using the DMRG indices. More...

double	getTwoDMA_HAM (const int cnt1, const int cnt2, const int cnt3, const int cnt4) const
	Get a 2DM_A term, using the HAM indices. More...

double	getTwoDMB_HAM (const int cnt1, const int cnt2, const int cnt3, const int cnt4) const
	Get a 2DM_B term, using the HAM indices. More...

double	get1RDM_HAM (const int cnt1, const int cnt2) const
	Get a 1-RDM term, using the HAM indices. More...

double	spin_density_ham (const int cnt1, const int cnt2) const
	Get a spin-density term, using the HAM indices. More...

void	FillSite (TensorT denT, TensorL Ltens, TensorF0 F0tens, TensorF1 F1tens, TensorS0 S0tens, TensorS1 **S1tens)
	Fill the 2DM terms with as second site index denT->gIndex() More...

void	correct_higher_multiplicities ()
	After the whole 2-RDM is filled, a prefactor for higher multiplicities should be applied.

double	trace () const
	Return the double trace of 2DM-A (should be N(N-1)) More...

double	energy () const
	Calculate the energy based on the 2DM-A. More...

void	print_noon () const
	Print the natural orbital occupation numbers.

void	save () const
	Save the TwoDMs to disk.

void	read ()
	Load the TwoDMs from disk.

void	save_HAM (const string filename) const
	Save the 2-RDM-A to disk in Hamiltonian indices. More...

void	write2DMAfile (const string filename) const
	Write the 2-RDM-A to a file. More...

void	mpi_allreduce ()
	Add the 2-RDM elements of all MPI processes.

Detailed Description

TwoDM class.

Author: Sebastian Wouters sebas.nosp@m.tian.nosp@m.woute.nosp@m.rs@g.nosp@m.mail..nosp@m.com

Date: June 13, 2013

The TwoDM class stores the result of a converged DMRG calculation. With the 2DM
$\Gamma_{(\alpha \sigma) (\beta \tau) ; (\gamma \sigma) (\delta \tau)} = \braket{ a^{\dagger}_{\alpha \sigma} a^{\dagger}_{\beta \tau} a_{\delta \tau} a_{\gamma \sigma} }$
we can define two spin-reduced versions of interest:
$\Gamma^{2A}_{\alpha \beta ; \gamma \delta} = \sum_{\sigma \tau} \Gamma_{(\alpha \sigma) (\beta \tau) ; (\gamma \sigma) (\delta \tau)}$
$\Gamma^{2B}_{\alpha \beta ; \gamma \delta} = \sum_{\sigma} \left( \Gamma_{(\alpha \sigma) (\beta \sigma) ; (\gamma \sigma) (\delta \sigma)} - \Gamma_{(\alpha \sigma) (\beta -\sigma) ; (\gamma \sigma) (\delta -\sigma)} \right)$ .
Because the wave-function belongs to a certain Abelian irrep, $I_{\alpha} \otimes I_{\beta} \otimes I_{\gamma} \otimes I_{\delta} = I_{trivial}$ must be valid before the corresponding element $\Gamma^{A,B}_{\alpha \beta ; \gamma \delta}$ is non-zero.

We can also define spin-densities in the spin-ensemble as:

$\begin{eqnarray*} \Gamma^{spin}_{ij} & = & \frac{3(1 - \delta_{S,0})}{(S+1)(2S+1)} \sum_{S^z} S^z \braket{ S S^z \mid a^{\dagger}_{i \uparrow} a_{j \uparrow} - a^{\dagger}_{i \downarrow} a_{j \downarrow} \mid S S^z } \\ & = & \frac{3(1 - \delta_{S,0})}{2(S+1)} \left[ ( 2 - N_{elec} ) \Gamma^1_{ij} - \sum_r \Gamma^{2A}_{ir;rj} - \sum_r \Gamma^{2B}_{ir;rj} \right] \end{eqnarray*}$

The normalization factor is chosen so that $trace( \Gamma^{spin} ) = 2 S$ .

Definition at line 50 of file TwoDM.h.

Constructor & Destructor Documentation

CheMPS2::TwoDM::TwoDM	(	const SyBookkeeper *	denBKIn,
		const Problem *	ProbIn
	)

Constructor.

Parameters

denBKIn	Symmetry sector bookkeeper
ProbIn	The problem to be solved

Definition at line 39 of file TwoDM.cpp.

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Member Function Documentation

double CheMPS2::TwoDM::energy ( ) const

Calculate the energy based on the 2DM-A.

Returns: The energy calculated as 0.5*trace(2DM-A * Ham)

Definition at line 216 of file TwoDM.cpp.

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void CheMPS2::TwoDM::FillSite	(	TensorT *	denT,
		TensorL ***	Ltens,
		TensorF0 ****	F0tens,
		TensorF1 ****	F1tens,
		TensorS0 ****	S0tens,
		TensorS1 ****	S1tens
	)

Fill the 2DM terms with as second site index denT->gIndex()

Parameters

denT	DMRG site-matrices
Ltens	Ltensors
F0tens	F0tensors
F1tens	F1tensors
S0tens	S0tensors
S1tens	S1tensors

Definition at line 444 of file TwoDM.cpp.

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double CheMPS2::TwoDM::get1RDM_DMRG	(	const int	cnt1,
		const int	cnt2
	)		const

Get a 1-RDM term, using the DMRG indices.

Parameters

cnt1	the first index
cnt2	the second index

Returns: the desired value

Definition at line 127 of file TwoDM.cpp.

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double CheMPS2::TwoDM::get1RDM_HAM	(	const int	cnt1,
		const int	cnt2
	)		const

Get a 1-RDM term, using the HAM indices.

Parameters

cnt1	the first index
cnt2	the second index

Returns: the desired value

Definition at line 184 of file TwoDM.cpp.

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double CheMPS2::TwoDM::getTwoDMA_DMRG	(	const int	cnt1,
		const int	cnt2,
		const int	cnt3,
		const int	cnt4
	)		const

Get a 2DM_A term, using the DMRG indices.

Parameters

cnt1	the first index
cnt2	the second index
cnt3	the third index
cnt4	the fourth index

Returns: the desired value

Definition at line 97 of file TwoDM.cpp.

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double CheMPS2::TwoDM::getTwoDMA_HAM	(	const int	cnt1,
		const int	cnt2,
		const int	cnt3,
		const int	cnt4
	)		const

Get a 2DM_A term, using the HAM indices.

Parameters

cnt1	the first index
cnt2	the second index
cnt3	the third index
cnt4	the fourth index

Returns: the desired value

Definition at line 164 of file TwoDM.cpp.

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double CheMPS2::TwoDM::getTwoDMB_DMRG	(	const int	cnt1,
		const int	cnt2,
		const int	cnt3,
		const int	cnt4
	)		const

Get a 2DM_B term, using the DMRG indices.

Parameters

cnt1	the first index
cnt2	the second index
cnt3	the third index
cnt4	the fourth index

Returns: the desired value

Definition at line 112 of file TwoDM.cpp.

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double CheMPS2::TwoDM::getTwoDMB_HAM	(	const int	cnt1,
		const int	cnt2,
		const int	cnt3,
		const int	cnt4
	)		const

Get a 2DM_B term, using the HAM indices.

Parameters

cnt1	the first index
cnt2	the second index
cnt3	the third index
cnt4	the fourth index

Returns: the desired value

Definition at line 174 of file TwoDM.cpp.

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void CheMPS2::TwoDM::save_HAM ( const string filename ) const

Save the 2-RDM-A to disk in Hamiltonian indices.

Parameters

filename The filename to store the 2-RDM at

Definition at line 278 of file TwoDM.cpp.

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double CheMPS2::TwoDM::spin_density_dmrg	(	const int	cnt1,
		const int	cnt2
	)		const

Get a spin-density term, using the DMRG indices.

Parameters

cnt1	the first index
cnt2	the second index

Returns: the desired value

Definition at line 143 of file TwoDM.cpp.

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double CheMPS2::TwoDM::spin_density_ham	(	const int	cnt1,
		const int	cnt2
	)		const

Get a spin-density term, using the HAM indices.

Parameters

cnt1	the first index
cnt2	the second index

Returns: the desired value

Definition at line 194 of file TwoDM.cpp.

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double CheMPS2::TwoDM::trace ( ) const

Return the double trace of 2DM-A (should be N(N-1))

Returns: Double trace of 2DM-A

Definition at line 204 of file TwoDM.cpp.

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void CheMPS2::TwoDM::write2DMAfile ( const string filename ) const

Write the 2-RDM-A to a file.

param filename where to write the 2-RDM-A elements to

Definition at line 372 of file TwoDM.cpp.

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

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation