netket._src.symmetry.translation_coset_filter.TranslationCosetFilter

class netket._src.symmetry.translation_coset_filter.TranslationCosetFilter

Bases: LabeledRepresentationCosetFilter

Fourier filter for the coset G/H of two translation representations.

Subclass of LabeledRepresentationCosetFilter specialised for translation groups: characters are Bloch factors e^{-ik·d} rather than values from a character table.

The full-group projector decomposes as:

P_G(k) = projector_refinement(k) @ sub_rep.projector(k)

Obtained via:

C = full_rep.coset_filter(sub_rep)

Inheritance

Attributes

full_rep

The full-group representation G.

irrep_labels

Full-group irrep labels (delegates to full_rep.irrep_labels).

k_points

Full-group Bloch momenta (delegates to full_rep.k_points).

lattice

Underlying lattice (same for both reps).

n_coset_reps

len(G) / len(H) — number of coset representatives.

sub_rep

The subgroup representation H.

Methods

chars(k)

Complex Bloch factors e^{-ik·d_c} for each coset representative c.

Parameters:

k – Bloch momentum — scalar (1D) or sequence (nD), one value per active axis of full_rep.

Return type:

ndarray

Returns:

Complex array of shape (P,).

coset_filter(subgroup)

Build the next coset filter in a refinement chain.

Delegates to sub_rep.coset_filter(subgroup), so the result has full_rep = self.sub_rep and sub_rep = subgroup:

C = rep_d4.coset_filter(rep_c4).coset_filter(rep_c2)
# equivalent to: rep_c4.coset_filter(rep_c2)

See LabeledRepresentation.coset_filter for the full documentation.

Return type:

LabeledRepresentationCosetFilter

projector_refinement(k=None, *, label=None, atol=1e-15)

Build the coset Fourier filter F_C(k).

Exactly one of k or label must be supplied.

Parameters:

• k – Bloch momentum.

• label (str | None) – Irrep label from irrep_labels.

• atol (float) – Drop terms with abs(coefficient) < atol.

Raises:

• TypeError – if neither or both of k and label are supplied.

• ValueError – if label is unknown.

Return type:

DiscreteJaxOperator