SU2 Operators

Operator factories and local gauge-invariant bases for SU(2) lattice gauge models.

Operator factories and gauge-invariant local bases for SU(2) lattice models.

edlgt.operators.SU2_operators.SU2_dressed_site_operators(spin, pure_theory, lattice_dim, background=0, n_flavors=None)[source]

Build SU(2) dressed-site operators using the hardcoded rishon construction.

Parameters:

  • spin (float) – Maximum rishon spin representation.

  • pure_theory (bool) – If True, exclude matter fields.

  • lattice_dim (int) – Number of spatial lattice dimensions (1, 2, or 3).

  • background (int, optional) – Maximum background-charge irrep included at each site.

  • n_flavors (int, optional) – Number of matter flavors. Defaults to 1 for matter theories. Multi-flavor operators are not yet implemented; passing n_flavors > 1 raises NotImplementedError.

Returns:

Dictionary of dressed-site operators used by the SU(2) model builders.

Return type:

dict

edlgt.operators.SU2_operators.SU2_gen_dressed_site_operators(spin, pure_theory, lattice_dim, background=0, n_flavors=None)[source]

Build SU(2) dressed-site operators using the generalized rishon construction.

Parameters:

  • spin (float) – Maximum rishon spin representation.

  • pure_theory (bool) – If True, exclude matter fields.

  • lattice_dim (int) – Number of spatial lattice dimensions (1, 2, or 3).

  • background (int, optional) – Maximum background-charge irrep included at each site.

  • n_flavors (int, optional) – Number of matter flavors. Defaults to 1 for matter theories. Multi-flavor operators are not yet implemented; passing n_flavors > 1 raises NotImplementedError.

Returns:

Dictionary of dressed-site operators for the generalized SU(2) model.

Return type:

dict

edlgt.operators.SU2_operators.SU2_check_gauss_law(gauge_basis, gauss_law_op, threshold=1e-14)[source]

Validate an SU(2) gauge-invariant basis against a Gauss-law operator.

Parameters:

  • gauge_basis (scipy.sparse.csr_matrix) – Basis matrix whose columns span the candidate gauge-invariant subspace.

  • gauss_law_op (scipy.sparse.csr_matrix) – Local Gauss-law operator.

  • threshold (float, optional) – Numerical tolerance used in the checks.

Return type:

None

Raises:

  • TypeError – If inputs are not sparse matrices.

  • ValueError – If the basis is not isometric/projective or does not lie in the Gauss-law kernel.

edlgt.operators.SU2_operators.SU2_gauge_invariant_states(s_max, pure_theory, lattice_dim, background=0, n_flavors=None)[source]

Construct local SU(2) gauge-invariant basis states and basis matrices.

Parameters:

  • s_max (float) – Maximum spin irrep used for the rishon Hilbert spaces.

  • pure_theory (bool) – If True, exclude matter fields.

  • lattice_dim (int) – Number of spatial lattice dimensions.

  • background (int, optional) – Maximum background-charge irrep included at the site.

  • n_flavors (int, optional) – Number of matter flavors. Each flavor contributes one independent SU(2) doublet on the site (4 fermion-occupation states). Defaults to 1 for matter theories and is ignored when pure_theory=True.

Returns:

(gauge_basis, gauge_states) dictionaries for bulk and border site classes. When background != 0, exact background-resolved entries keyed by (bg, label) are added alongside the legacy aggregate label keys.

Return type:

tuple

edlgt.operators.SU2_operators.SU2_gauge_invariant_operators(spin, pure_theory, lattice_dim, background=0, use_generic_operators=False)[source]

Project truncated SU(2) dressed-site operators onto GI local bases.

Parameters:

  • spin (float) – Gauge-link spin representation.

  • pure_theory (bool) – If True, exclude matter fields.

  • lattice_dim (int) – Number of spatial dimensions.

  • background (scalar, optional) – Maximum background irrep included in the local basis.

  • use_generic_operators (bool, optional) – If True, force the generalized truncated operator construction. Otherwise the hardcoded construction is used for spin < 1 and the generalized one for higher truncations.

Returns:

Dictionary keyed by (label, op_name). When background == 0, label is a string such as "site" or "site_mx". When background != 0, label is an exact basis label of the form (bg, geom_label).

Return type:

dict