pyblock.symmetry¶

pyblock.symmetry.symmetry¶

Symmetry related data structures.

class pyblock.symmetry.symmetry.DirectProdGroup(*args)¶

Bases: object

Irreducible representation for symmetry formed by direct product of sub-symmetries.

Attributes:

irs : list(Group): A list of irreducible representations for sub-symmetries.
ng : int: Number of sub-symmetries.

sub_group(idx)¶: Return a subgroup of this object, given a list of indices.

class pyblock.symmetry.symmetry.HashIrrep(ir)¶

Bases: object

Base class for irreducible representation, supporting hashing.

class pyblock.symmetry.symmetry.PGC1(ir)¶

Bases: pyblock.symmetry.symmetry.PointGroup

\(C_1\) point group.

Cached = [None]¶

InverseElem = array([0])¶

IrrepNames = ['A']¶

Table = array([[0]])¶

class pyblock.symmetry.symmetry.PGC2(ir)¶

Bases: pyblock.symmetry.symmetry.PGCI

\(C_2\) point group.

IrrepNames = ['A', 'B']¶

class pyblock.symmetry.symmetry.PGC2H(ir)¶

Bases: pyblock.symmetry.symmetry.PGC2V

\(C_{2h}\) point group.

IrrepNames = ['Ag', 'Au', 'Bu', 'Bg']¶

class pyblock.symmetry.symmetry.PGC2V(ir)¶

Bases: pyblock.symmetry.symmetry.PointGroup

\(D_{c2v}\) point group.

Cached = [None, None, None, None]¶

InverseElem = array([0, 1, 2, 3])¶

IrrepNames = ['A1', 'B1', 'B2', 'A2']¶

Table = array([[0, 1, 2, 3], [1, 0, 3, 2], [2, 3, 0, 1], [3, 2, 1, 0]])¶

class pyblock.symmetry.symmetry.PGCI(ir)¶

Bases: pyblock.symmetry.symmetry.PointGroup

\(C_i\) point group.

Cached = [None, None]¶

InverseElem = array([0, 1])¶

IrrepNames = ['Ag', 'Au']¶

Table = array([[0, 1], [1, 0]])¶

class pyblock.symmetry.symmetry.PGCS(ir)¶

Bases: pyblock.symmetry.symmetry.PGCI

\(C_s\) point group.

IrrepNames = ["A'", "A''"]¶

class pyblock.symmetry.symmetry.PGD2(ir)¶

Bases: pyblock.symmetry.symmetry.PGC2V

\(D_2\) point group.

IrrepNames = ['A1', 'B3', 'B2', 'B1']¶

class pyblock.symmetry.symmetry.PGD2H(ir)¶

Bases: pyblock.symmetry.symmetry.PointGroup

\(D_{2h}\) point group.

Cached = [None, None, None, None, None, None, None, None]¶

InverseElem = array([0, 1, 2, 3, 4, 5, 6, 7])¶

IrrepNames = ['Ag', 'B3u', 'B2u', 'B1g', 'B1u', 'B2g', 'B3g', 'Au']¶

Table = array([[0, 1, 2, 3, 4, 5, 6, 7], [1, 0, 3, 2, 5, 4, 7, 6], [2, 3, 0, 1, 6, 7, 4, 5], [3, 2, 1, 0, 7, 6, 5, 4], [4, 5, 6, 7, 0, 1, 2, 3], [5, 4, 7, 6, 1, 0, 3, 2], [6, 7, 4, 5, 2, 3, 0, 1], [7, 6, 5, 4, 3, 2, 1, 0]])¶

class pyblock.symmetry.symmetry.ParticleN(ir)¶

Bases: pyblock.symmetry.symmetry.HashIrrep

Irreducible representation for particle number symmetry.

CachedM = []¶

CachedP = []¶

static clebsch_gordan(a, b, c)¶

multiplicity¶

class pyblock.symmetry.symmetry.PointGroup(ir)¶

Bases: pyblock.symmetry.symmetry.HashIrrep

Base class for irreducible representation for point group symmetry.

Attributes:

Table : rank-2 numpy.ndarray: Mutiplication table of the group.
InverseElem : rank-1 numpy.ndarray: Inverse Element of each element in the group.
IrrepNames : list(str): Name of each irreducible representation in the group.

InverseElem = array([], dtype=int64)¶

IrrepNames = []¶

Table = array([], shape=(0, 0), dtype=int64)¶

static clebsch_gordan(a, b, c)¶

multiplicity¶

class pyblock.symmetry.symmetry.SU2(s)¶

Bases: pyblock.symmetry.symmetry.HashIrrep

Irreducible representation for SU(2) spin symmetry.

Cached = []¶

static clebsch_gordan(a, b, c)¶: Return rank-3 numpy.ndarray for CG coefficients with all possible projected quantum numbers.

j¶: SU(2) spin quantum number.

multiplicity¶

to_multi()¶

class pyblock.symmetry.symmetry.SU2Proj(s, sz)¶

Bases: pyblock.symmetry.symmetry.SU2

Irreducible representation for SU(2) spin symmetry with extra projected spin label.

Cached = []¶

copy()¶

jz¶: SU(2) projected spin quantum number.

multiplicity¶

static random_from_multi(multi)¶

to_multi()¶

class pyblock.symmetry.symmetry.SZ(sz)¶

Bases: pyblock.symmetry.symmetry.HashIrrep

Irreducible representation for projected spin symmetry.

CachedM = []¶

CachedP = []¶

static clebsch_gordan(a, b, c)¶

multiplicity¶

pyblock.symmetry.symmetry.point_group(pg_name)¶: Return point group class corresponding to the point group name.