Irreps#

spgrep_modulation.irreps.project_eigenmode_representation(eigenmode_representation: numpy.ndarray[Any, numpy.dtype[numpy.complex128]], primitive: phonopy.structure.cells.Primitive, primitive_symmetry: phonopy.structure.symmetry.Symmetry, primitive_qpoint: numpy.ndarray[Any, numpy.dtype[numpy.float64]], method: Literal['Neto', 'random'] = 'Neto', rtol: float = 1e-05, atol: float = 1e-06) → tuple[list[numpy.ndarray[Any, numpy.dtype[numpy.complex128]]], list[numpy.ndarray[Any, numpy.dtype[numpy.complex128]]], numpy.ndarray[Any, numpy.dtype[numpy.int32]]][source]#

Decompose representation matrices by eigenmodes into irreps.

Parameters

  • eigenmode_representation (array, (order, num_atoms, 3, num_atoms, 3)) – Representation matrices formed by phonon eigenmodes

  • primitive (phonopy.structure.cells.Primitive) – phonopy’s primitive object

  • primitive_symmetry (phonopy.structure.symmetry.Symmetry) – phonopy’s Symmetry object for primitive cell

  • primitive_qpoint (array, (3, )) – q vector in primitive’s dual basis vectors

  • method (str, 'Neto' or 'random') – ‘Neto’: construct irreps from a fixed chain of subgroups of little co-group ‘random’: construct irreps by numerically diagonalizing a random matrix commute with regular representation

  • rtol (float) – Relative tolerance for comparing float values

  • atol (float) – Absolute tolerance to distinguish difference eigenvalues

Returns

  • all_basis (list) – all_basis[i] is list of independent basis vectors with (dim, num_atoms, 3) forming irreps[i]. Note: phase chosen to be consistent with definition of phonopy’s dynamical matrix

  • irreps (list of irrep (little_order, dim, dim))

  • mapping_little_group – list of indices for little group.

spgrep_modulation.irreps.get_eigenmode_representation(primitive: phonopy.structure.cells.Primitive, primitive_symmetry: phonopy.structure.symmetry.Symmetry, primitive_qpoint: numpy.ndarray[Any, numpy.dtype[numpy.float64]]) → numpy.ndarray[Any, numpy.dtype[numpy.complex128]][source]#

Compute representation matrix for eigenmodes.

\[\Gamma_{\kappa'\mu'; \kappa\mu}^{\mathbf{q}}(g) := \exp \left( -i \mathbf{R}_{g} \mathbf{q} \cdot \mathbf{h}_{g}(\kappa) \right) [\mathbf{R}_{g}]_{\mu'\mu} \delta_{ g\kappa, \kappa' }\]
Parameters

  • primitive (phonopy.structure.cells.Primitive) – phonopy’s primitive object

  • primitive_symmetry (phonopy.structure.symmetry.Symmetry) – phonopy’s Symmetry object for primitive cell

  • primitive_qpoint (array, (3, )) – q vector in primitive’s dual basis vectors

Returns

rep – Representation matrices

Return type

array, (order, num_atoms, 3, num_atoms, 3)