SU2 Yang Mills LGT Model Class

SU(2) lattice gauge-theory model helper with hardcoded and generalized operator constructions.

class edlgt.models.SU2_model.SU2_Model(spin, pure_theory, bg_list=None, sectors=None, use_generic_model=False, n_flavors=None, **kwargs)

Bases: QuantumModel

SU(2) lattice gauge model with hardcoded and generalized operator sets.

Initialize the SU(2) model and construct its symmetry sector.

Parameters:

• spin (float or str = integrated) – Gauge-link spin representation.

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

• bg_list (list, optional) – Optional background-charge specification.

• sectors (list, optional) – Global matter-sector labels. In the current SU(2) matter models this selects the total particle-number sector. For the integrated 1D model, the exact global Delta_Z_tot = 0 constraint is added automatically on top of that particle sector.

• use_generic_model (bool, optional) – If True, force the generalized operator construction.

• n_flavors (int, optional) – Number of matter flavors. Defaults to 1 for matter theories. Multi-flavor Hamiltonians are not yet implemented; passing n_flavors > 1 raises NotImplementedError. The flavored gauge-invariant local basis is still available via SU2_gauge_invariant_states().

• **kwargs – Arguments forwarded to QuantumModel.

build_Hamiltonian(g, m=None, theta=0.0, lambda_noise=0.0, dtype_mode='auto')

Dispatch to the hardcoded or generalized SU(2) Hamiltonian builder.

Parameters:

dtype_mode (str or bool, optional) – "auto", "real", "complex", or legacy bool flag.

build_base_Hamiltonian(g, m=None, theta=0.0, lambda_noise=0.0, dtype_mode='auto')

Assemble the hardcoded low-spin SU(2) Hamiltonian.

Parameters:

• g (float) – Gauge coupling.

• m (float, optional) – Bare mass parameter.

• theta (float, optional) – Topological-angle parameter.

• lambda_noise (float, optional) – Optional Gauss-law-violating noise strength.

• dtype_mode (str or bool, optional) – "auto", "real", "complex", or legacy bool flag.

build_gen_Hamiltonian(g, m=None, dtype_mode='auto')

Assemble the generalized SU(2) Hamiltonian.

Parameters:

• g (float) – Gauge coupling.

• m (float, optional) – Bare mass parameter.

• dtype_mode (str or bool, optional) – "auto", "real", "complex", or legacy bool flag.

build_integrated_Hamiltonian(g, m, dtype_mode='auto')

Assemble the integrated-gauge 1D SU2 Hamiltonian.

Parameters:

dtype_mode (str or bool, optional) – "auto", "real", "complex", or legacy bool flag.

reconstruct_Casimir_from_matter(single_obs_name='N_single', delta_corr_obs_name='Delta_Z_Delta_Z', flip_corr_obs_name='Sp_r_Sm_g_Sm_r_Sp_g', flop_corr_obs_name='Sm_r_Sp_g_Sp_r_Sm_g', state=None, state_index=None, dynamics=False, compute_single_obs=True, compute_pair_corr=True, print_values=True)

Reconstruct integrated 1D SU(2) link Casimirs from matter observables.

Notes

For the current integrated 1D SU(2) model with OBC and no static charges, the electric energy can be written in terms of the link Casimirs

T^2_n = (sum_{k=0}^n vec(T)_k)^2.

In the local integrated basis, the single-site and pairwise pieces are

T_k^2 = 3/4 * N_single(k)

and

2 vec(T)_i . vec(T)_j = Delta_Z(i) Delta_Z(j) / 8 + Sp_r_Sm_g(i) Sm_r_Sp_g(j) + Sm_r_Sp_g(i) Sp_r_Sm_g(j).

get_fermionic_string_correlator(state=None, state_index=None, dynamics=False, print_values=False)

Measure the gauge-invariant fermionic string correlator matrix.

Notes

This implementation is currently defined for the 1D truncated SU(2) dressed-site model, both in the hardcoded j=1/2 construction and in the generic truncated construction whenever the projected operator set exposes the effective singlet operators Qpx_dag, Qmx, and the scalar intermediate transporter W.

A first attempt kept two explicit color labels at the endpoints and produced a (2L, 2L) matrix. After projection to the gauge-invariant dressed-site basis, however, the red and green endpoint channels become identical. This is a direct consequence of working in the local gauge-invariant dressed-site basis, where Gauss’ law has already been solved site by site. The physically meaningful covariance matrix therefore has one effective fermionic mode per dressed site, i.e. size (L, L).

Pedagogically, the point is that the local dressed-site basis does not keep bare color states such as |r> and |g> as independent physical states. Instead, matter and rishons are first combined into local SU(2)-invariant singlets. For a matter doublet and a rishon doublet, the local color space decomposes as 2 x 2 = 1 + 3: the projection keeps the singlet channel and discards the triplet. The two endpoint color components are therefore just two representatives of the same surviving singlet channel, and their difference is projected out.

For i < j we measure

C_ij = 1/4 <Qpx_dag(i) W(i+1) ... W(j-1) Qmx(j)>

The factor 1/4 appears because, inside the projected basis, the singlet endpoint operators satisfy Qpx_dag = 2 Fpx_eff_dag and Qmx = 2 Fmx_eff. The intermediate color contraction is already absorbed locally into the scalar dressed-site operator W. On the diagonal we store

C_ii = <N_tot(i)> / 2

because each effective site mode carries half of the total on-site fermion number.

measure_fermionic_nongaussianity(state=None, state_index=None, dynamics=False, print_value=True, eig_tol=1e-10)

Measure the fermionic non-Gaussianity from the string correlator.

check_symmetries()

Check link-symmetry constraints on measured observables.

overlap_QMB_state(name)

Return predefined benchmark SU(2) basis configurations.

Parameters:

name (str) – Label of a reference configuration.

Returns:

Configuration in the model basis.

Return type:

numpy.ndarray

SU2_Hamiltonian_couplings(g, m=None, theta=0.0)

Set SU(2) Hamiltonian couplings from physical parameters.

Parameters:

• g (float) – Gauge coupling.

• m (float, optional) – Bare mass parameter (used when matter fields are present).

• theta (float, optional) – Topological-angle parameter.

Returns:

Couplings are stored in self.coeffs.

Return type:

None

Notes

In the current convention, the Hamiltonian is rescaled so that the hopping term is dimensionless (as used in the project implementation and in PRX Quantum 5, 040309).

The rescaling summary used in the code is:

• hopping: original coupling 1/2 -> 2 * sqrt(2)

• electric term: original g0^2 / 2 -> 8 g^2 / 3

• magnetic term: rescaled convention factor applied in the model

• the symbol g in this implementation is used as the rescaled coupling (effectively a g^2 convention)

DFL-project convention (reference values often used in scripts):

• E = 8 * g / 3

• B = -3 / g

• t = 2 * sqrt(2)

String-breaking convention (alternative reference choice):

• E = g

• B = -1

• t = 1

build_local_Hamiltonian(g, m, R0)

Build a local effective Hamiltonian around one 1D site.

Parameters:

• g (float) – Gauge coupling.

• m (float) – Bare mass parameter.

• R0 (int) – Central lattice site.

get_mask(sites_list)

Build a boolean mask selecting the given sites.

local_parity_labels(wrt_site)

Local action of pure spatial inversion (left-right swap) on the 6d dressed-site SU(2) basis.

Basis labels: 0: V, J=(0,0) 1: V, J=(1/2,1/2) (link singlet) 2: (1/2,0,1/2) (matter + right link) 3: (1/2,1/2,0) (matter + left link) 4: P, J=(0,0) 5: P, J=(1/2,1/2) (link singlet)

Returns:

(loc_perm, loc_phase) where loc_perm contains the mapped local basis indices and loc_phase contains the corresponding phases (+1 or -1).

Return type:

tuple

get_parity_inversion_operator(wrt_site)

Construct the parity inversion operator in the current sector.

check_parity_inversion_operator()

Validate algebraic and dynamical properties of the parity operator.

print_state_config(config, amplitude=None)

Log a readable per-site decomposition of an SU(2) basis configuration.