Researchers show that a simple higher‑dimensional gauge model can host long‑lived, non‑thermal quantum states known as Quantum Many‑Body Scars. They find this by proving an approximate version of a spectrum‑generating algebra in a pure gauge ‘‘plaquette ladder’’ built from spin‑1 quantum links. The key step is a mapping that turns the ladder into a constrained spin chain, where the constraint spoils an exact symmetry but leaves an approximate one for some states.

The model is a spin‑1 Quantum Link Model on a ladder of L plaquettes. The authors focus on the case with no extra potential (V = 0) and use periodic boundary conditions. The original ladder obeys gauge constraints (Gauss’ law) and conservation of two winding numbers. By a dualization procedure they map the ladder to a one‑dimensional chain of spin‑1 variables. In that dual chain three‑site projectors Pn enforce the gauge constraint: they forbid certain neighbouring spin patterns. Within the constrained Hilbert space, the dual chain and the ladder are equivalent.

Without the projectors the dual Hamiltonian would be a simple sum of Sx operators and would have an exact SU(2) dynamical symmetry. In that free case an operator O† would raise energies by a fixed amount and generate towers of equally spaced eigenstates. With the projectors present that Lie algebra is broken. The authors show that a reduced, approximate version of the algebra survives on part of the spectrum. They define three collective operators (˜Hx, ˜Hy, ˜Hz) built from projected local spin raising and lowering terms, and introduce a ‘‘broken Casimir’’ operator ˜C = ˜Hx^2 + ˜Hy^2 + ˜Hz^2 to test for remnants of total‑spin structure.

To support the claim they compute diagnostics on finite systems (for example L = 10). The half‑system entanglement entropy S_{L/2} plotted versus energy reveals mid‑spectrum outlier states with unusually low entanglement. Those outliers appear to form nearly equally spaced levels in energy. The broken Casimir expectation values for the same eigenstates also show a family of outliers with approximately constant ˜C, consistent with the presence of approximate towers generated by the broken algebra. The authors note missing points at E = 0 due to a large degeneracy there that mixes states under exact diagonalization.