Global Abelian Symmetries

Filters and generators for global Abelian (U(1), Z2, and string-like) symmetry sectors.

Global Abelian symmetry filters for many-body configurations.

The functions in this module test and generate configuration subsets satisfying global U(1), Z2, or string-like diagonal symmetry constraints.

edlgt.symmetries.global_abelian_sym.check_global_sym(config, sym_op_diags, sym_sectors, sym_type_flag)

Check whether a configuration satisfies global Abelian symmetry sectors.

Parameters:

• config (numpy.ndarray) – Single many-body configuration (one local state label per site).

• sym_op_diags (numpy.ndarray) – Operator diagonals defining the symmetries. Shape is typically (n_sym, loc_dim) for uniform local spaces.

• sym_sectors (numpy.ndarray) – Target sector value for each symmetry generator.

• sym_type_flag (int) – Symmetry type selector: 0 for additive U(1), 1 for multiplicative Z2, and values >1 for element-wise string constraints.

Returns:

True if config belongs to the chosen sector.

Return type:

bool

edlgt.symmetries.global_abelian_sym.check_global_sym_sitebased(config, sym_op_diags, sym_sectors, sym_type_flag)

Site-based version of check_global_sym() for nonuniform local bases.

Parameters:

• config (numpy.ndarray) – Single many-body configuration.

• sym_op_diags (numpy.ndarray) – Site-resolved operator diagonals of shape (n_sym, n_sites, max(loc_dims)).

• sym_sectors (numpy.ndarray) – Target sector value for each symmetry generator.

• sym_type_flag (int) – Symmetry type selector: 0 for U(1), 1 for Z2.

Returns:

True if config belongs to the chosen sector.

Return type:

bool

edlgt.symmetries.global_abelian_sym.global_abelian_sector(loc_dims, sym_op_diags, sym_sectors, sym_type, configs=None)

Filter configurations by global Abelian symmetry constraints.

Parameters:

• loc_dims (numpy.ndarray) – Local Hilbert-space dimensions.

• sym_op_diags (numpy.ndarray) – Diagonals of symmetry generators. Can be site-independent or site-based.

• sym_sectors (numpy.ndarray or typing.Sequence) – Target sector values for the generators.

• sym_type (str) – Symmetry type code: "U" (U(1)), "Z" (Z2), or other values for string constraints.

• configs (numpy.ndarray, optional) – If provided, filter this existing configuration table instead of generating the full product basis.

Returns:

Configurations belonging to the requested global symmetry sector.

Return type:

numpy.ndarray

edlgt.symmetries.global_abelian_sym.global_sector_configs(loc_dims, glob_op_diags, glob_sectors, sym_type_flag)

Enumerate site-based global-symmetry configurations from the full basis.

Parameters:

• loc_dims (numpy.ndarray) – Local Hilbert-space dimensions.

• glob_op_diags (numpy.ndarray) – Site-resolved diagonals of global symmetry generators.

• glob_sectors (numpy.ndarray) – Target sector values.

• sym_type_flag (int) – Symmetry type selector used by check_global_sym_sitebased().

Returns:

Filtered configuration table.

Return type:

numpy.ndarray

edlgt.symmetries.global_abelian_sym.check_string_sym_sitebased(config, sym_op_diags, sym_sectors)

Check site-resolved string constraints for one configuration.

Parameters:

• config (numpy.ndarray) – Single many-body configuration.

• sym_op_diags (numpy.ndarray) – Site-resolved diagonals for the string constraints.

• sym_sectors (numpy.ndarray) – Target values for the string constraints.

Returns:

True if the configuration satisfies all string constraints.

Return type:

bool