#include <ham-mom.h>

Inheritance diagram for MomHamiltonian:

Collaboration diagram for MomHamiltonian:

Public Member Functions
	MomHamiltonian (int L, int Nu, int Nd, double J, double U)

virtual	~MomHamiltonian ()

void	BuildBase ()

void	BuildFullHam ()

virtual void	mvprod (double x, double y, double alpha) const

std::vector< double >	ExactDiagonalizeFull (bool calc_eigenvectors)

virtual std::vector< std::pair < int, double > >	ExactMomDiagonalizeFull (bool calc_eigenvectors)

void	GenerateData (double Ubegin, double Uend, double step, std::string filename)

std::string	print_bin (myint num) const

virtual void	BuildHam ()

int	getL () const

int	getNu () const

int	getNd () const

int	getDim () const

double	getJ () const

double	getU () const

void	setU (double)

myint	getBaseUp (unsigned int i) const

myint	getBaseDown (unsigned int i) const

virtual double	LanczosDiagonalize (int m=0)

virtual double	arpackDiagonalize ()

void	Print (bool list=false) const

void	PrintBase () const

void	PrintGroundstateVector () const

double	MemoryNeededFull () const

double	MemoryNeededLanczos () const

double	MemoryNeededArpack () const

virtual void	SaveToFile (const std::string filename) const

Static Public Member Functions
static int	CalcDim (int L, int N)

static int	CountBits (myint bits)

static std::string	print_bin (myint num, int bitcount)

Protected Member Functions
double	hopping (myint) const

int	interaction (int, int, int, int) const

void	SaveToFile (const std::string filename, double *data, int dim) const

int	CalcSign (int i, int j, myint a) const

Static Protected Member Functions
static void	Diagonalize (int dim, double mat, double eigs, bool calc_eigenvectors)

Protected Attributes
std::vector< std::vector < std::pair< int, int > > >	mombase

std::vector< std::unique_ptr < double[]> >	blockmat

int	L
	Number of sites. More...

int	Nu
	Number of up electrons. More...

int	Nd
	Number of down electrons. More...

double	J
	Hopping strength. More...

double	U
	On site interaction strength. More...

double *	ham
	Storage for the BareHamiltonian matrix. More...

int	dim
	Dimension of the BareHamiltonian matrix. More...

myint	Hb
	Hightest bit used. More...

int	Hbc
	the location of the highest bit More...

std::vector< myint >	baseUp
	vector to hold all bases ket's for up electrons More...

std::vector< myint >	baseDown
	vector to hold all bases ket's for down electrons More...

Detailed Description

This is the main (base) class. It calculates the full MomHamiltonian matrix for 1D Hubbard. It can both exact diagonlize or use a Lanczos algorithm to calculate the groundstate energy.

Author: Ward Poelmans wpoel.nosp@m.y86@.nosp@m.gmail.nosp@m..com

Definition at line 33 of file ham-mom.h.

Constructor & Destructor Documentation

MomHamiltonian::MomHamiltonian	(	int	L,
		int	Nu,
		int	Nd,
		double	J,
		double	U
	)

Constructor of the MomHamiltonian class

Parameters

L	Number of lattice sites
Nu	Number of Up Electrons
Nd	Number of Down Electrons
J	The hopping strengh
U	The onsite interaction strength

Definition at line 45 of file ham-mom.cpp.

MomHamiltonian::~MomHamiltonian ( )

virtual

Destructor of the MomHamiltonian class

Definition at line 52 of file ham-mom.cpp.

Member Function Documentation

double BareHamiltonian::arpackDiagonalize ( )

virtualinherited

Definition at line 436 of file bare-ham.cpp.

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void MomHamiltonian::BuildBase ( )

virtual

Builds all the up and down base kets in the momentum base Sort them so we have a block diagonal matrix according to total momentum

Reimplemented from BareHamiltonian.

Definition at line 60 of file ham-mom.cpp.

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void MomHamiltonian::BuildFullHam ( )

virtual

Builds the full MomHamiltonian matrix

Implements BareHamiltonian.

Definition at line 131 of file ham-mom.cpp.

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void BareHamiltonian::BuildHam ( )

virtualinherited

This method is always present and should build the Hamiltonian, either full or sparse

Definition at line 165 of file bare-ham.cpp.

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int BareHamiltonian::CalcDim	(	int	L,
		int	N
	)

staticinherited

Calculates the dimension for the up or down electron space. Basically, it calculates the N-combination out of L. This algorithm is not perfect, overflow can occur but should be no problem for our small problems.

Parameters

L	number of lattice sites
N	number of up or down electrons

Returns: the dimension of the up or down electron space

Definition at line 83 of file bare-ham.cpp.

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int BareHamiltonian::CalcSign	(	int	i,
		int	j,
		myint	a
	)		const

protectedinherited

Calculates the sign of the hop between site i and site j on ket a. Make sure that i < j!

Parameters

i	the first sp
j	the second sp
a	the ket to use

Returns: the sign of the hop

Definition at line 178 of file bare-ham.cpp.

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int BareHamiltonian::CountBits ( myint bits )

staticinherited

Counts the number of bits set. It uses the builtin gcc function __buildtin_popcount. You must compile with -march=native and it will then generate a POPCNT instruction on platforms that support it. Otherwise it will be slow. Consider using a different method here if you don't have the POPCNT instruction: there are fast SSSE3 and SSE2 ways to do this(google is your friend).

Parameters

bits	the myint of which to count the number of bits set

Returns: the number of bits set

Definition at line 106 of file bare-ham.cpp.

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void BareHamiltonian::Diagonalize	(	int	dim,
		double *	mat,
		double *	eigs,
		bool	calc_eigenvectors
	)

staticprotectedinherited

Helper for exact diagonalization: diagonalize the matrix given in mat with dimension dim, stores the eigenvalues in eigs and optionally the eigenvectors in mat

Parameters

dim	the dimension of the matrix
mat	the actual matrix (size: dim*dim)
eigs	array of size dim to store eigenvalues
calc_eigenvectors	whether or not the calculate the eigenvectors

Definition at line 681 of file bare-ham.cpp.

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std::vector< double > MomHamiltonian::ExactDiagonalizeFull ( bool calc_eigenvectors )

virtual

Exactly calculates the eigenvalues of the matrix. Needs lapack.

Parameters

calc_eigenvectors set to true to calculate the eigenvectors. The hamiltonian matrix is then overwritten by the vectors.

Returns: the vector of the sorted eigenvalues

Reimplemented from BareHamiltonian.

Definition at line 310 of file ham-mom.cpp.

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std::vector< std::pair< int, double > > MomHamiltonian::ExactMomDiagonalizeFull ( bool calc_eigenvectors )

virtual

Diagonalize the block diagonal matrix. Needs lapack. Differs from MomHamiltonian::ExactDiagonalizeFull that is diagonalize block per block and keeps the momentum associated with each eigenvalue.

Parameters

calc_eigenvectors set to true to calculate the eigenvectors. The hamiltonian matrix is then overwritten by the vectors.

Returns: a vector of pairs. The first member of the pair is the momentum, the second is the eigenvalue. The vector is sorted to the eigenvalues.

Definition at line 338 of file ham-mom.cpp.

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void MomHamiltonian::GenerateData	(	double	Ubegin,
		double	Uend,
		double	step,
		std::string	filename
	)

This methods calculates the eigenvalues for a range of U values. The interval is [Ubegin, Uend] with a stepsize of step. The resulting data is written to a file in the HDF5 file format.

Parameters

Ubegin	the startpoint for U
Uend	the endpoint for U. We demand Ubegin < Uend
step	the stepsize to use for U
filename	the name of the file write to written the eigenvalues to

Definition at line 374 of file ham-mom.cpp.

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myint BareHamiltonian::getBaseDown ( unsigned int i ) const

inherited

Getter for the i base down ket

Parameters

i	the number of the base ket

Returns: the base ket

Definition at line 270 of file bare-ham.cpp.

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myint BareHamiltonian::getBaseUp ( unsigned int i ) const

inherited

Getter for the i base up ket

Parameters

i	the number of the base ket

Returns: the base ket

Definition at line 260 of file bare-ham.cpp.

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int BareHamiltonian::getDim ( ) const

inherited

Getter for the dimension of the BareHamiltonian matrix

Returns: dimension of the BareHamiltonian matrix

Definition at line 223 of file bare-ham.cpp.

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double BareHamiltonian::getJ ( ) const

inherited

Getter for the hopping strength

Returns: the hopping strength

Definition at line 232 of file bare-ham.cpp.

int BareHamiltonian::getL ( ) const

inherited

Getter for the number of lattice sites

Returns: the number of lattice sites

Definition at line 196 of file bare-ham.cpp.

int BareHamiltonian::getNd ( ) const

inherited

Getter for the number of down electrons

Returns: the number of down electrons

Definition at line 214 of file bare-ham.cpp.

int BareHamiltonian::getNu ( ) const

inherited

Getter for the number of up electrons

Returns: the number of up electrons

Definition at line 205 of file bare-ham.cpp.

double BareHamiltonian::getU ( ) const

inherited

Getter for the onsite interaction strength

Returns: the onsite interaction strength

Definition at line 241 of file bare-ham.cpp.

double MomHamiltonian::hopping ( myint ket ) const

protected

private method used to see if a hopping between state a and b is possible and with which sign. Only for 1D Hubbard.

Parameters

ket	the ket to use

Returns: matrix element of the hopping term between the ket and the bra. You still have to multiply this with the hopping strength J

Definition at line 262 of file ham-mom.cpp.

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int MomHamiltonian::interaction	(	int	a,
		int	b,
		int	c,
		int	d
	)		const

protected

private method to calculate the interaction between a 2 particle ket and bra

Parameters

a	the first base vector of the bra
b	the second base vector of the bra
c	the first base vector of the ket
d	the second base vector of the ket

Returns: matrix element of the interaction term between the ket and the bra. You still have to multiply this with the interaction strength U and divide by the lattice length L

Definition at line 177 of file ham-mom.cpp.

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double BareHamiltonian::LanczosDiagonalize ( int m = 0 )

virtualinherited

Calculates the lowest eigenvalue of the BareHamiltonian matrix using the lanczos algorithm. Needs lapack.

Parameters

m	an optional estimate for the lanczos space size

Returns: the lowest eigenvalue

Definition at line 313 of file bare-ham.cpp.

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double BareHamiltonian::MemoryNeededArpack ( ) const

inherited

Calculates the amount of memory needed for the calculation if we use the arpack. It doesn't include the program code and stuff.

Returns: the amount of memory needed in bytes

Definition at line 643 of file bare-ham.cpp.

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double BareHamiltonian::MemoryNeededFull ( ) const

inherited

Calculates the amount of memory needed for the calculation of all eigenvalues using the exact method. It doesn't include the program code and stuff.

Returns: the amount of memory needed in bytes

Definition at line 591 of file bare-ham.cpp.

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double BareHamiltonian::MemoryNeededLanczos ( ) const

inherited

Calculates the amount of memory needed for the calculation if we use the lanczos method. It doesn't include the program code and stuff.

Returns: the amount of memory needed in bytes

Definition at line 617 of file bare-ham.cpp.

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void MomHamiltonian::mvprod	(	double *	x,
		double *	y,
		double	alpha
	)		const

virtual

Matrix vector product with MomHamiltonian: y = ham*x + alpha*y

Parameters

x	the input vector
y	the output vector
alpha	the scaling value

Implements BareHamiltonian.

Definition at line 285 of file ham-mom.cpp.

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void BareHamiltonian::Print ( bool list = false ) const

inherited

Prints the full BareHamiltonian matrix to stdout

Definition at line 410 of file bare-ham.cpp.

std::string BareHamiltonian::print_bin ( myint num ) const

inherited

Print a int in binary form to a string. Prints a much as needed to represent the current system.

Parameters

num	the myint to print in binary form

Returns: a string with the binary representation of num

Definition at line 138 of file bare-ham.cpp.

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std::string BareHamiltonian::print_bin	(	myint	num,
		int	bitcount
	)

staticinherited

Print a int in binary form to a string. It only prints the bitcount least significant bits

Parameters

num	the myint to print in binary form
bitcount	the number of bits to print (starting from the LSB)

Returns: a string with the binary representation of num

Definition at line 118 of file bare-ham.cpp.

void BareHamiltonian::PrintBase ( ) const

inherited

Print the basis set used.

Definition at line 429 of file bare-ham.cpp.

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void BareHamiltonian::PrintGroundstateVector ( ) const

inherited

Prints the groundstate in function of the basis vectors Only gives meanfull output after running BareHamiltonian::ExactDiagonalizeFull(true)

Definition at line 295 of file bare-ham.cpp.

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void BareHamiltonian::SaveToFile ( const std::string filename ) const

virtualinherited

Save the hamiltonian matrix to a file in the HDF5 format

Parameters

filename the name of the file to write to

Definition at line 727 of file bare-ham.cpp.

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void BareHamiltonian::SaveToFile	(	const std::string	filename,
		double *	data,
		int	dim
	)		const

protectedinherited

Save a array to a file in the HDF5 format

Parameters

filename	the name of the file to write to
data	a pointer to the array to write to a file
dim	the size of the array

Definition at line 741 of file bare-ham.cpp.

void BareHamiltonian::setU ( double myU )

inherited

Set the value of U

Parameters

myU	the value of U

Definition at line 250 of file bare-ham.cpp.

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Member Data Documentation

std::vector<myint> BareHamiltonian::baseDown

protectedinherited

vector to hold all bases ket's for down electrons

Definition at line 138 of file bare-ham.h.

std::vector<myint> BareHamiltonian::baseUp

protectedinherited

vector to hold all bases ket's for up electrons

Definition at line 136 of file bare-ham.h.

std::vector< std::unique_ptr<double []> > MomHamiltonian::blockmat

protected

Definition at line 57 of file ham-mom.h.

int BareHamiltonian::dim

protectedinherited

Dimension of the BareHamiltonian matrix.

Definition at line 128 of file bare-ham.h.

double* BareHamiltonian::ham

protectedinherited

Storage for the BareHamiltonian matrix.

Definition at line 126 of file bare-ham.h.

myint BareHamiltonian::Hb

protectedinherited

Hightest bit used.

Definition at line 131 of file bare-ham.h.

int BareHamiltonian::Hbc

protectedinherited

the location of the highest bit

Definition at line 133 of file bare-ham.h.

double BareHamiltonian::J

protectedinherited

Hopping strength.

Definition at line 122 of file bare-ham.h.

int BareHamiltonian::L

protectedinherited

Number of sites.

Definition at line 116 of file bare-ham.h.

std::vector< std::vector< std::pair<int,int> > > MomHamiltonian::mombase

protected

Definition at line 55 of file ham-mom.h.

int BareHamiltonian::Nd

protectedinherited

Number of down electrons.

Definition at line 120 of file bare-ham.h.

int BareHamiltonian::Nu

protectedinherited

Number of up electrons.

Definition at line 118 of file bare-ham.h.

double BareHamiltonian::U

protectedinherited

On site interaction strength.

Definition at line 124 of file bare-ham.h.

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

Public Member Functions

Static Public Member Functions

Protected Member Functions

Static Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation