QED Operators

Operator factories and local gauge-invariant bases for U(1) lattice gauge models.

Operator factories and gauge-invariant local bases for U(1) (QED) models.

edlgt.operators.QED_operators.QED_dressed_site_operators(spin, pure_theory, lattice_dim, U='ladder', fermionic=True, background=0, check_gauss_law=False)[source]

Build dressed-site QED operators for 1D, 2D, or 3D lattices.

Parameters:

spin (int) – Gauge-link spin truncation (local link dimension 2*spin + 1).
pure_theory (bool) – If True, build the pure-gauge operator set (no matter fields).
lattice_dim (int) – Number of spatial lattice dimensions (supported: 1, 2, 3).
U (str, optional) – Rishon-shift convention passed to QED_rishon_operators() (typically "ladder" or "spin").
fermionic (bool, optional) – If True, use fermionic matter/rishon parity conventions.
background (int, optional) – Maximum absolute static background charge included at each site. 0 disables the background degree of freedom.
check_gauss_law (bool, optional) – If True, run internal consistency checks on the constructed local Gauss-law operators.

Returns:

Dictionary of dressed-site operators used by the QED model builders.

Return type:

dict

edlgt.operators.QED_operators.QED_gauge_invariant_states(spin, pure_theory, lattice_dim, background=0, get_only_bulk=False)[source]

Construct local gauge-invariant QED basis states and basis matrices.

Parameters:

spin (int) – Gauge-link spin truncation.
pure_theory (bool) – If True, exclude matter fields.
lattice_dim (int) – Number of spatial dimensions.
background (int, optional) – Maximum absolute static background charge included at the site.
get_only_bulk (bool, optional) – If True, keep only bulk-compatible site subsets when classifying border/corner configurations.

Returns:

(gauge_basis, gauge_states) dictionaries. gauge_basis stores sparse basis matrices (full local basis -> gauge-invariant subspace) and gauge_states stores the corresponding local configurations. When background > 0, exact background-resolved entries keyed by (bg, label) are added alongside the legacy aggregate label keys.

Return type:

tuple

edlgt.operators.QED_operators.QED_gauge_invariant_operators(spin, pure_theory, lattice_dim, background=0, get_only_bulk=False, U='ladder', fermionic=True)[source]

Project QED dressed-site operators onto all compatible GI local bases.

Parameters:

spin (int) – Gauge-link spin truncation.
pure_theory (bool) – If True, exclude matter fields.
lattice_dim (int) – Number of spatial dimensions.
background (int, optional) – Maximum absolute background charge included in the local basis.
get_only_bulk (bool, optional) – Forwarded to QED_gauge_invariant_states().
U (str, optional) – Rishon-shift convention passed to QED_dressed_site_operators().
fermionic (bool, optional) – Fermionic-parity convention passed to QED_dressed_site_operators().

Returns:

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

Return type:

dict

edlgt.operators.QED_operators.QED_rishon_operators(spin, pure_theory, U, fermionic=True, background=0)[source]

Build single-rishon operators for a truncated U(1) quantum link model.

The local basis is the electric-field eigenbasis with dimension “2*spin + 1” and eigenvalues “E = -spin, …, +spin” (in increasing order). The operator “U” is implemented as a one-step shift in this basis (chosen so that it raises “E” by one unit where defined).

If “fermionic=True”, rishons are treated as fermionic modes via a local parity operator “P = (-1)**n” and the convention:

Zp     = U @ P
Zm_dag = U
Zm     = Zm_dag.T
Zp_dag = Zp.T

Convenience composites used in corner/plaquette constructions are also provided (e.g. “Zp_P”, “P_Zm_dag”).

Parameters:

spin (int) – Truncation parameter (local dimension 2*spin + 1).
pure_theory (bool) – Included for API consistency and validation.
U (str) – Shift amplitude convention. Supported values are "ladder" and "spin".
fermionic (bool, optional) – If True, include parity and enforce fermionic anticommutation checks.

Returns:

Sparse operator dictionary including P, U, rishon creation and annihilation operators, and electric-field operators.

Return type:

dict

edlgt.operators.QED_operators.QED_check_gauss_law(spin, pure_theory, lattice_dim, gauss_law_ops, background=0, threshold=1e-15)[source]

Validate a local QED gauge-invariant basis against Gauss-law constraints.

Parameters:

spin (int) – Gauge-link spin truncation.
pure_theory (bool) – If True, check the pure-gauge local basis.
lattice_dim (int) – Number of spatial lattice dimensions.
gauss_law_ops (dict) – Dictionary of local Gauss-law operators keyed by site type.
background (int, optional) – Maximum absolute static background charge included in the local basis.
threshold (float, optional) – Numerical tolerance used in the consistency checks.

Return type:

None

Raises:

TypeError – If input argument types are invalid.
ValueError – If the basis is not isometric/projective or does not satisfy Gauss law.

edlgt.operators.QED_operators.QED_plq_site_operators(spin, pure_theory, lattice_dim, U='ladder')[source]

Build plaquette-local operators for the 2D pure-gauge QED formulation.

The four dressed-site factors inside a plaquette are ordered as:

  4|     3|
-- o ---- o --
   |      |
  1|     2|
-- o ---- o --
   |      |