Module to obtain the density matrix by diagonalizing an orthogonalized Hamiltonian. More...

Functions/Subroutines
subroutine, public	prg_build_density_t0 (ham_bml, rho_bml, threshold, bndfil, eigenvalues_out)
	Builds the density matrix from \( H_0 \) for zero electronic temperature. \( \rho = C \Theta(\mu I - \epsilon) C^{\dagger} \) Where, \( C \) is the matrix eigenvector and \( \epsilon \) is the matrix eigenvalue. \( \Theta() \) is the Heaviside function. More...

subroutine, public	prg_build_density_t (ham_bml, rho_bml, threshold, bndfil, kbt, ef, eigenvalues_out)
	Builds the density matrix from \( H_0 \) for electronic temperature T. \( \rho = C f(\mu I - \epsilon) C^{\dagger} \) Where, \( C \) is the matrix eigenvector and \( \epsilon \) is the matrix eigenvalue. \( f \) is the Fermi function. More...

subroutine, public	prg_build_density_t_fulldata (ham_bml, rho_bml, threshold, bndfil, kbt, ef, eigenvalues_out, evects_bml, fvals)
	Builds the density matrix from \( H_0 \) for electronic temperature T. \( \rho = C f(\mu I - \epsilon) C^{\dagger} \) Where, \( C \) is the matrix eigenvector and \( \epsilon \) is the matrix eigenvalue. \( f \) is the Fermi function. More...

subroutine, public	prg_build_density_t_ed (ham_bml, rho_bml, evects_bml, threshold, bndfil, kbt, ef, evals, dvals, hindex, llsize, verbose)
	Builds the density matrix from \( H_0 \) for electronic temperature T. \( \rho = C f(\mu I - \epsilon) C^{\dagger} \) Where, \( C \) is the matrix eigenvector and \( \epsilon \) is the matrix eigenvalue. \( f \) is the Fermi function. More...

subroutine, public	prg_get_evalsdvalsevects (ham_bml, threshold, hindex, llsize, evals, dvals, evects_bml, verbose)
	Gets the eigenvalues and eigenvectors and the core contribution to each eigenvalue (dvals) . More...

subroutine, public	prg_build_density_fromevalsandevects (evects_bml, evals, rho_bml, threshold, bndfil, kbt, ef, verbose)
	Builds the density matrix from the evects and evals for electronic temperature T. More...

subroutine, public	prg_build_density_t_fermi (ham_bml, rho_bml, threshold, kbt, ef, verbose, drho)
	Builds the density matrix from \( H_0 \) for electronic temperature T. \( \rho = C f(\mu I - \epsilon) C^{\dagger} \) Where, \( C \) is the matrix eigenvector and \( \epsilon \) is the matrix eigenvalue. \( f \) is the Fermi function. In this routine the Fermi level is passed as an argument. More...

subroutine, public	prg_build_atomic_density (rhoat_bml, numel, hindex, spindex, norb, bml_type)
	Builds the atomic density matrix. \( \rho_{ii} = mathcal{Z}_{ii} \) Where, \( mathcal{Z}_{ii} \) is the number of electrons for orbital i. More...

subroutine, public	prg_get_flevel (eigenvalues, kbt, bndfil, tol, Ef, err)
	Routine to compute the Fermi level given a set of eigenvalues and a temperature. It applies the Bisection method over the function: \( g(\mu) = \sum_k 2 f(\epsilon_k - \mu) - N = 0 \) Where \( f(\epsilon_k - \mu) = \frac{1}{1+\exp{(\epsilon_k - \mu)/(k_bT)}}\). More...

subroutine, public	prg_get_flevel_nt (eigenvalues, kbt, bndfil, tol, ef, err, verbose)
	Routine to compute the Fermi level given a set of eigenvalues and a temperature. It applies the Newton-Raphson method over the function: \( g(\mu) = \sum_k 2 f(\epsilon_k - \mu) - N = 0 \) Where \( f(\epsilon_k - \mu) = \frac{1}{1+\exp{(\epsilon_k - \mu)/(k_bT)}}\). More...

subroutine, public	prg_get_eigenvalues (ham_bml, eigenvalues, verbose)
	Gets the eigenvalues of the Orthogonalized Hamiltonian. More...

subroutine, public	prg_check_idempotency (mat_bml, threshold, idempotency)
	To check the idempotency error of a matrix. This is calculated as the Frobenius norm of \( (A - A^2) \). More...

real(dp) function	fermi (e, ef, kbt)
	Gives the Fermi distribution value for energy e. More...

real(dp) function	dfermi (e, ef, kbt)
	Gives the gradient of Fermi distribution w.r.t. ef. More...

subroutine, public	prg_toeigenspace (mat_bml, matEig_bml, evects_bml, threshold, verbose)
	Change an operator into the eigenspace representation. More...

subroutine, public	prg_tocanonicalspace (mat_bml, matCan_bml, evects_bml, threshold, verbose)
	Change an operator into the eigenspace representation. More...

subroutine, public	canon_dm_prt (P1, H1, Nocc, T, Q, e, mu0, m, HDIM)

subroutine	eig (A, Q, ee, TYPE, HDIM)

Variables
integer, parameter	dp = kind(1.0d0)

Detailed Description

Module to obtain the density matrix by diagonalizing an orthogonalized Hamiltonian.

Function/Subroutine Documentation

◆ canon_dm_prt()

subroutine, public prg_densitymatrix_mod::canon_dm_prt	(	real(prec), dimension(hdim,hdim), intent(out)	P1,
		real(prec), dimension(hdim,hdim), intent(in)	H1,
		real(prec), intent(in)	Nocc,
		real(prec), intent(in)	T,
		real(prec), dimension(hdim,hdim), intent(in)	Q,
		real(prec), dimension(hdim), intent(in)	e,
		real(prec), intent(in)	mu0,
		integer, intent(in)	m,
		integer, intent(in)	HDIM
	)

Definition at line 1126 of file prg_densitymatrix_mod.F90.

◆ dfermi()

real(dp) function prg_densitymatrix_mod::dfermi	(	real(dp), intent(in)	e,
		real(dp), intent(in)	ef,
		real(dp), intent(in)	kbt
	)

private

Gives the gradient of Fermi distribution w.r.t. ef.

Parameters

e	Energy.
ef	Fermi energy.

Definition at line 1020 of file prg_densitymatrix_mod.F90.

◆ eig()

subroutine prg_densitymatrix_mod::eig	(	real(prec), dimension(hdim,hdim), intent(in)	A,
		real(prec), dimension(hdim,hdim), intent(out)	Q,
		real(prec), dimension(hdim), intent(out)	ee,
		character(1), intent(in)	TYPE,
		integer, intent(in)	HDIM
	)

private

Definition at line 1192 of file prg_densitymatrix_mod.F90.

◆ fermi()

real(dp) function prg_densitymatrix_mod::fermi	(	real(dp), intent(in)	e,
		real(dp), intent(in)	ef,
		real(dp), intent(in)	kbt
	)

private

Gives the Fermi distribution value for energy e.

Parameters

e	Energy.
ef	Fermi energy.

Definition at line 1004 of file prg_densitymatrix_mod.F90.

◆ prg_build_atomic_density()

subroutine, public prg_densitymatrix_mod::prg_build_atomic_density	(	type(bml_matrix_t), intent(inout)	rhoat_bml,
		real(dp), dimension(:), intent(in)	numel,
		integer, dimension(:,:), intent(in)	hindex,
		integer, dimension(:), intent(in)	spindex,
		integer, intent(in)	norb,
		character(len=*), intent(in)	bml_type
	)

Builds the atomic density matrix. \( \rho_{ii} = mathcal{Z}_{ii} \) Where, \( mathcal{Z}_{ii} \) is the number of electrons for orbital i.

Parameters

rhoat	Output atomic diagonal density matrix,
hindex	Start and end index for every atom in the system.
numel	Number of electrons per specie. It runs over the specie index.
spindex	Specie index.
norbs	Number of orbitals.

Definition at line 650 of file prg_densitymatrix_mod.F90.

◆ prg_build_density_fromevalsandevects()

subroutine, public prg_densitymatrix_mod::prg_build_density_fromevalsandevects	(	type(bml_matrix_t), intent(inout)	evects_bml,
		real(dp), dimension(*), intent(in)	evals,
		type(bml_matrix_t), intent(inout)	rho_bml,
		real(dp), intent(in)	threshold,
		real(dp), intent(in)	bndfil,
		real(dp), intent(in)	kbt,
		real(dp), intent(inout)	ef,
		integer, intent(in)	verbose
	)

Builds the density matrix from the evects and evals for electronic temperature T.

Parameters

evects_bml	Eigenvectors.
evals	Eigenvalues.
threshold	Threshold for sparse matrix algebra.
bndfil	Filing factor.
kbt	Electronic temperature.
ef	Fermi level.
verbose	Verbosity level.

Definition at line 481 of file prg_densitymatrix_mod.F90.

◆ prg_build_density_t()

subroutine, public prg_densitymatrix_mod::prg_build_density_t	(	type(bml_matrix_t), intent(in)	ham_bml,
		type(bml_matrix_t), intent(inout)	rho_bml,
		real(dp), intent(in)	threshold,
		real(dp), intent(in)	bndfil,
		real(dp), intent(in)	kbt,
		real(dp), intent(inout)	ef,
		real(dp), dimension(:), intent(out), optional, allocatable	eigenvalues_out
	)

Builds the density matrix from \( H_0 \) for electronic temperature T. \( \rho = C f(\mu I - \epsilon) C^{\dagger} \) Where, \( C \) is the matrix eigenvector and \( \epsilon \) is the matrix eigenvalue. \( f \) is the Fermi function.

Parameters

ham_bml	Input Orthogonalized Hamiltonian matrix.
rho_bml	Output density matrix,
threshold	Threshold for sparse matrix algebra.
bndfil	Filing factor.
kbt	Electronic temperature.
ef	Fermi level.
eigenvalues_out	Output the eigenvalues.

Warning: This does not solve the generalized eigenvalue problem. The Hamiltonian that comes in has to be preorthogonalized.

Definition at line 122 of file prg_densitymatrix_mod.F90.

◆ prg_build_density_t0()

subroutine, public prg_densitymatrix_mod::prg_build_density_t0	(	type(bml_matrix_t), intent(in)	ham_bml,
		type(bml_matrix_t), intent(inout)	rho_bml,
		real(8), intent(in)	threshold,
		real(8), intent(in)	bndfil,
		real(dp), dimension(:), intent(out), optional, allocatable	eigenvalues_out
	)

Builds the density matrix from \( H_0 \) for zero electronic temperature. \( \rho = C \Theta(\mu I - \epsilon) C^{\dagger} \) Where, \( C \) is the matrix eigenvector and \( \epsilon \) is the matrix eigenvalue. \( \Theta() \) is the Heaviside function.

Parameters

ham_bml	Input Orthogonalized Hamiltonian matrix.
rho_bml	Output density matrix.
threshold	Threshold for sparse matrix algebra.
bndfil	Filing factor.
eigenvalues_out	Output the eigenvalues.

Warning: This does not solve the generalized eigenvalue problem. The Hamiltonian that comes in has to be preprg_orthogonalized.

Definition at line 41 of file prg_densitymatrix_mod.F90.

◆ prg_build_density_t_ed()

subroutine, public prg_densitymatrix_mod::prg_build_density_t_ed	(	type(bml_matrix_t), intent(in)	ham_bml,
		type(bml_matrix_t), intent(inout)	rho_bml,
		type(bml_matrix_t), intent(inout)	evects_bml,
		real(dp), intent(in)	threshold,
		real(dp), intent(in)	bndfil,
		real(dp), intent(in)	kbt,
		real(dp), intent(inout)	ef,
		real(dp), dimension(:), intent(inout), allocatable	evals,
		real(dp), dimension(:), intent(inout), allocatable	dvals,
		integer, dimension(:,:), intent(in), allocatable	hindex,
		integer, intent(in)	llsize,
		integer, intent(in)	verbose
	)

Builds the density matrix from \( H_0 \) for electronic temperature T. \( \rho = C f(\mu I - \epsilon) C^{\dagger} \) Where, \( C \) is the matrix eigenvector and \( \epsilon \) is the matrix eigenvalue. \( f \) is the Fermi function.

Parameters

ham_bml	Input Orthogonalized Hamiltonian matrix.
rho_bml	Output density matrix,
threshold	Threshold for sparse matrix algebra.
bndfil	Filing factor.
kbt	Electronic temperature.
ef	Fermi level.
evals	Output the eigenvalues.
fvals	Output the occupancies.
dvals	Contribution to population from every evect.
core_indices	Indices in the core.

Warning: This does not solve the generalized eigenvalue problem. The Hamiltonian that comes in has to be orthogonalized.

Definition at line 292 of file prg_densitymatrix_mod.F90.

◆ prg_build_density_t_fermi()

subroutine, public prg_densitymatrix_mod::prg_build_density_t_fermi	(	type(bml_matrix_t), intent(in)	ham_bml,
		type(bml_matrix_t), intent(inout)	rho_bml,
		real(dp), intent(in)	threshold,
		real(dp), intent(in)	kbt,
		real(dp), intent(in)	ef,
		integer, intent(in), optional	verbose,
		real(dp), intent(inout), optional	drho
	)

Builds the density matrix from \( H_0 \) for electronic temperature T. \( \rho = C f(\mu I - \epsilon) C^{\dagger} \) Where, \( C \) is the matrix eigenvector and \( \epsilon \) is the matrix eigenvalue. \( f \) is the Fermi function. In this routine the Fermi level is passed as an argument.

Parameters

ham_bml	Input Orthogonalized Hamiltonian matrix.
rho_bml	Output density matrix,
threshold	Threshold for sparse matrix algebra.

Warning: This does not solve the generalized eigenvalue problem. The Hamiltonian that comes in has to be preorthogonalized.

Definition at line 566 of file prg_densitymatrix_mod.F90.

◆ prg_build_density_t_fulldata()

subroutine, public prg_densitymatrix_mod::prg_build_density_t_fulldata	(	type(bml_matrix_t), intent(in)	ham_bml,
		type(bml_matrix_t), intent(inout)	rho_bml,
		real(dp), intent(in)	threshold,
		real(dp), intent(in)	bndfil,
		real(dp), intent(in)	kbt,
		real(dp), intent(inout)	ef,
		real(dp), dimension(:), intent(inout), allocatable	eigenvalues_out,
		type(bml_matrix_t), intent(inout)	evects_bml,
		real(dp), dimension(:), intent(inout), allocatable	fvals
	)

Builds the density matrix from \( H_0 \) for electronic temperature T. \( \rho = C f(\mu I - \epsilon) C^{\dagger} \) Where, \( C \) is the matrix eigenvector and \( \epsilon \) is the matrix eigenvalue. \( f \) is the Fermi function.

Parameters

ham_bml	Input Orthogonalized Hamiltonian matrix.
rho_bml	Output density matrix,
threshold	Threshold for sparse matrix algebra.
bndfil	Filing factor.
kbt	Electronic temperature.
ef	Fermi level.
eigenvalues_out	Output the eigenvalues.
evects_bml	Output the eigenvectors.
fvals	Output the occupancies.

Warning: This does not solve the generalized eigenvalue problem. The Hamiltonian that comes in has to be preorthogonalized.

Definition at line 207 of file prg_densitymatrix_mod.F90.

◆ prg_check_idempotency()

subroutine, public prg_densitymatrix_mod::prg_check_idempotency	(	type(bml_matrix_t), intent(in)	mat_bml,
		real(dp), intent(in)	threshold,
		real(dp), intent(out)	idempotency
	)

To check the idempotency error of a matrix. This is calculated as the Frobenius norm of \( (A - A^2) \).

Parameters

mat_bml	Some bml matrix
idempotency	(Output value of the idempotency error)

Definition at line 980 of file prg_densitymatrix_mod.F90.

◆ prg_get_eigenvalues()

subroutine, public prg_densitymatrix_mod::prg_get_eigenvalues	(	type(bml_matrix_t), intent(in)	ham_bml,
		real(dp), dimension(:), intent(inout), allocatable	eigenvalues,
		integer, intent(in)	verbose
	)

Gets the eigenvalues of the Orthogonalized Hamiltonian.

Parameters

ham_bml	Input Orthogonalized Hamiltonian matrix.
eigenvalues	Output eigenvalues of the system.
verbose	Verbosity level.

Definition at line 935 of file prg_densitymatrix_mod.F90.

◆ prg_get_evalsdvalsevects()

subroutine, public prg_densitymatrix_mod::prg_get_evalsdvalsevects	(	type(bml_matrix_t), intent(in)	ham_bml,
		real(dp), intent(in)	threshold,
		integer, dimension(:,:), intent(in), allocatable	hindex,
		integer, intent(in)	llsize,
		real(dp), dimension(:), intent(inout), allocatable	evals,
		real(dp), dimension(:), intent(inout), allocatable	dvals,
		type(bml_matrix_t), intent(inout)	evects_bml,
		integer, intent(in)	verbose
	)

Gets the eigenvalues and eigenvectors and the core contribution to each eigenvalue (dvals) .

Parameters

ham_bml	Input Orthogonalized Hamiltonian matrix.
threshold	Threshold for sparse matrix algebra.
hindex	Start and end index for every atom in the system.
llsize	Number of atoms in the core of the graph part.
evals	Eigenvalues.
dvals	Contribution to population from every evect.
evects_bml	Output the eigenvectors.

Warning: This does not solve the generalized eigenvalue problem. The Hamiltonian that comes in has to be orthogonalized.

Definition at line 386 of file prg_densitymatrix_mod.F90.

◆ prg_get_flevel()

subroutine, public prg_densitymatrix_mod::prg_get_flevel	(	real(dp), dimension(:), intent(in)	eigenvalues,
		real(dp), intent(in)	kbt,
		real(dp), intent(in)	bndfil,
		real(dp)	tol,
		real(dp), intent(inout)	Ef,
		logical, intent(inout)	err
	)

Routine to compute the Fermi level given a set of eigenvalues and a temperature. It applies the Bisection method over the function: \( g(\mu) = \sum_k 2 f(\epsilon_k - \mu) - N = 0 \) Where \( f(\epsilon_k - \mu) = \frac{1}{1+\exp{(\epsilon_k - \mu)/(k_bT)}}\).

Parameters

eigenvalues	Eigenvalues of the system ( \( \{ \epsilon_k \} \)).
kbt	Temperature times the Boltzmann's constant ( \( k_bT \)).
bndfil	Filing factor ( \( N_{el}/(2*N_{orbs})\)).
tol	Tolerance for the bisection method.
Ef	Fermi level ( \( \mu \)).
err	Error logical variable

Definition at line 775 of file prg_densitymatrix_mod.F90.

◆ prg_get_flevel_nt()

subroutine, public prg_densitymatrix_mod::prg_get_flevel_nt	(	real(dp), dimension(:), intent(in)	eigenvalues,
		real(dp), intent(in)	kbt,
		real(dp), intent(in)	bndfil,
		real(dp), intent(in)	tol,
		real(dp), intent(inout)	ef,
		logical, intent(inout)	err,
		integer, intent(in), optional	verbose
	)

Routine to compute the Fermi level given a set of eigenvalues and a temperature. It applies the Newton-Raphson method over the function: \( g(\mu) = \sum_k 2 f(\epsilon_k - \mu) - N = 0 \) Where \( f(\epsilon_k - \mu) = \frac{1}{1+\exp{(\epsilon_k - \mu)/(k_bT)}}\).

Parameters

eigenvalues	Eigenvalues of the system ( \( \{ \epsilon_k \} \)).
kbt	Temperature times the Boltzmann's constant ( \( k_bT \)).
bndfil	Filing factor ( \( N_{el}/(2*N_{orbs})\)).
tol	Tolerance for the bisection method.
Ef	Fermi level ( \( \mu \)).
err	Error logical variable

Definition at line 847 of file prg_densitymatrix_mod.F90.

◆ prg_tocanonicalspace()

subroutine, public prg_densitymatrix_mod::prg_tocanonicalspace	(	type(bml_matrix_t), intent(in)	mat_bml,
		type(bml_matrix_t), intent(inout)	matCan_bml,
		type(bml_matrix_t), intent(in)	evects_bml,
		real(dp), intent(in)	threshold,
		integer, intent(in), optional	verbose
	)

Change an operator into the eigenspace representation.

This routine performs \( O_{eig} = U O U^{t} \), where operator U is the unitary

Definition at line 1090 of file prg_densitymatrix_mod.F90.

◆ prg_toeigenspace()

subroutine, public prg_densitymatrix_mod::prg_toeigenspace	(	type(bml_matrix_t), intent(in)	mat_bml,
		type(bml_matrix_t), intent(inout)	matEig_bml,
		type(bml_matrix_t), intent(in)	evects_bml,
		real(dp), intent(in)	threshold,
		integer, intent(in), optional	verbose
	)

Change an operator into the eigenspace representation.

This routine performs \( O_{eig} = U^{T} O U \), where operator U is the unitary transformations constructed from the eigenvectors of a Hamiltonian

Parameters

mat_bml	Operator to be transformed
matEig_bml	Output operator after transformation
evects_bml	Eigenvectors matrix (U)
threshold	Threshold parameter \verbose Verbosity level

Definition at line 1046 of file prg_densitymatrix_mod.F90.

Variable Documentation

◆ dp

integer, parameter prg_densitymatrix_mod::dp = kind(1.0d0)

private

Definition at line 19 of file prg_densitymatrix_mod.F90.

Functions/Subroutines

Variables

Detailed Description

Function/Subroutine Documentation

◆ canon_dm_prt()

◆ dfermi()

◆ eig()

◆ fermi()

◆ prg_build_atomic_density()

◆ prg_build_density_fromevalsandevects()

◆ prg_build_density_t()

◆ prg_build_density_t0()

◆ prg_build_density_t_ed()

◆ prg_build_density_t_fermi()

◆ prg_build_density_t_fulldata()

◆ prg_check_idempotency()

◆ prg_get_eigenvalues()

◆ prg_get_evalsdvalsevects()

◆ prg_get_flevel()

◆ prg_get_flevel_nt()

◆ prg_tocanonicalspace()

◆ prg_toeigenspace()

Variable Documentation

◆ dp