Non-stabilizerness and entanglement in (2+1) -dimensional SU(2) lattice gauge theory using tensor networks

We study non-stabilizerness (magic) in the ground state of (2+1) -dimensional SU(2) Hamiltonian lattice gauge theory with matter, formulated in the dressed-site basis in the hardcore-gluon truncation and restricted to the zero baryon-number sector. Using matrix product states, we compute three facets of magic: the second-order stabilizer Rényi entropy (SRE) M 2, its non-local component M 2 NL, and a lower bound in terms of the anti-flatness F of the entanglement spectrum. We also prove a stronger form of the sandwich relation: - 2(1-4F) M 2 NL M 2; the lower bound rests on a stronger inequality that we obtain for arbitrary Schmidt bases and rank, thus resolving the open problem of finding the maximal lower bound. We emphasize a structural distinction that makes the non-local quantities the physically preferred diagnostics: whereas the full SRE depends on the (non-unique) encoding of the gauge-invariant local Hilbert space into qubits, both the non-local magic and the anti-flatness are invariant under site-local re-encodings and are therefore intrinsic to the state and bipartition. By varying the gauge coupling on lattices up to 6 times 6 with bond dimension up to 128, we find that the non-local magic furnishes a sharper and more bond-dimension-friendly probe of the gauge-matter delocalization crossover compared to the full SRE or the gauge-invariant entanglement entropy, retaining a clear signal at bond dimensions well below those needed to converge the ground state itself.