Local (Link) Abelian Symmetries

Filters and generators for link-local Abelian symmetry constraints.

Local/link Abelian symmetry filters for many-body configurations.

This module provides checks and configuration generators for symmetry sectors defined by link-local two-site constraints, as commonly used in lattice gauge models with open or periodic geometries.

edlgt.symmetries.link_abelian_sym.check_link_sym(config, sym_op_diags, sym_sectors, pair_list)[source]

Check whether a configuration satisfies link Abelian symmetry sectors.

Parameters:

config (numpy.ndarray) – Single many-body configuration.
sym_op_diags (numpy.ndarray) – Link-symmetry generator diagonals with shape (n_dirs, 2, loc_dim) for uniform local spaces.
sym_sectors (numpy.ndarray) – Target sector value for each lattice direction.
pair_list (typing.Sequence) – For each lattice direction, a 2-column integer array listing the site pairs constrained by that symmetry.

Returns:

True if config belongs to the chosen sector.

Return type:

bool

edlgt.symmetries.link_abelian_sym.check_link_sym_sitebased(config, sym_op_diags, sym_sectors, pair_list)[source]

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

Parameters:

config (numpy.ndarray) – Single many-body configuration.
sym_op_diags (numpy.ndarray) – Site-resolved diagonals with shape (n_dirs, 2, n_sites, max(loc_dims)).
sym_sectors (numpy.ndarray) – Target sector value for each lattice direction.
pair_list (typing.Sequence) – For each lattice direction, a 2-column integer array listing the site pairs constrained by that symmetry.

Returns:

True if config belongs to the chosen sector.

Return type:

bool

edlgt.symmetries.link_abelian_sym.link_abelian_sector(loc_dims, sym_op_diags, sym_sectors, pair_list)[source]

Generate configurations belonging to a link Abelian symmetry sector.

Parameters:

loc_dims (numpy.ndarray) – Local Hilbert-space dimensions.
sym_op_diags (numpy.ndarray) – Link-symmetry generator diagonals (uniform or site-based representation).
sym_sectors (numpy.ndarray or typing.Sequence) – Target sector values for the link generators.
pair_list (typing.Sequence) – Pair list describing which site pairs are checked in each direction.

Returns:

(sector_indices, sector_configs) with linear basis indices and the corresponding site configurations.

Return type:

tuple

edlgt.symmetries.link_abelian_sym.link_sector_configs(loc_dims, link_op_diags, link_sectors, pair_list)[source]

Enumerate configurations satisfying site-based link symmetry constraints.

Parameters:

loc_dims (numpy.ndarray) – Local Hilbert-space dimensions.
link_op_diags (numpy.ndarray) – Site-resolved link-symmetry generator diagonals.
link_sectors (numpy.ndarray) – Target sector values for the link generators.
pair_list (typing.Sequence) – Pair list describing which site pairs are checked in each direction.

Returns:

Filtered configuration table.

Return type:

numpy.ndarray