principia_materia.hamiltonian.electron_hamiltonian module

class principia_materia.hamiltonian.electron_hamiltonian.ElectronHamiltonian(structure, mesh=None, pg='C1', nspin=1, nelect=None, fermi=None, ncor=0, U=0, units='eV', verbosity=1, tol=1e-06)

Bases: Hamiltonian

Parameters:

  • nelect (int, optional, default to None) – Number of valence electrons.

  • fermi (float, optional, default to None) – Fermy energy, in unit of eV.

  • ncor (int, optional, default to None) – Number of correlated orbitals.

  • U (int, optional, default to 0) – The Coulumb hamiltonian term U.

diagonalize_hamiltonians(hamiltonians_matrices, UPLO='L')

Diagonalize and compute the eigenvalues hamiltonians in reciprocal space.

Returns:

  • eigenvalues (array of float, shape(N, nspin, norbitals))

  • eigenvectors (array of float, shape(N, nspin, norbitals, norbitals))

get_embeded_self_energy()

Embed the self-energy minus the dc in a matrix the size of the Hamiltonian.

get_fermi_energy()

Get Fermi energy.

Returns:

fermi – The Fermi energy.

Return type:

float

get_hamiltonian_matrices_at_kpoints(kpoints)

Get hamiltonian matrices at k-points

Parameters:

kpoints (array of float or Fraction, shape(dim, ) or shape(N, dim)) – k-points.

Returns:

hamiltonians_matrices – Interaction matrices.

Return type:

array of complex, shape(norbitals, norbitals) or shape(N, norbitals, norbitals)

get_state()

Get insulator/metal state of the Hamiltonian.

get_total_energy()

Get the total energy of the Hamiltonian.

hartree_fock(nd=0, nscf=40, tol=1e-05, mix=0.7, perturb=True, dc=False)

Hartree Fock.

set_density_matrix()

Compute the density matrix of the Hamiltonian.

set_fermi_energy(replace=False, maxiter=200, raise_exception=False)

Compute Fermi energy with binary search and tetrahedron method.

Parameters:

  • replace (bool, optional, default to False) – Re-compute Fermi energy when attribute _fermi is not None.

  • maxiter (int, optional, default to 200) – The maximum number of iterations to search for the Fermi energy.

  • raise_exception (bool, optional, default to False) – Whether to raise an exception when the maximum iteration is reached before the error tolerence is reached.

set_hamiltonian(hamiltonian)

Set electron hamiltonian.

Parameters:

hamiltonian (ModelHamiltonian) – ModelHamiltonian object.

_hamiltonian

ModelHamiltonian object.

Type:

ModelHamiltonian

set_nd(nd, max_loop=200, tol=0.0001)

Adjust number d-electrons.

Adjust the double-counting to get the desired number of d-electrons while maintaining the proper density. This algo creates a a scalar function which computes nd for a given dc while always adjusting the fermi energy to give the correct density. This function is then manually bounded and then sent to brentq in order to find the root.

set_self_energy(self_energy, fermi=None, dc=None)
set_total_energy()

Compute the total energy of the Hamiltonian with tetrahedron method.