Quantum many-body scars are eigenstates of a non-integrable Hamiltonian that refuse to thermalize. In a system where the eigenstate thermalization hypothesis says every eigenstate should look thermal — with local expectation values matching the microcanonical ensemble — scars stand out as a discrete set of states with anomalously low entanglement and persistent oscillations in local observables. They are islands of order in a sea of ergodicity. The natural question is what protects them.
Sharma and Tripathi (arXiv 2602.22397, February 2026) identify a hidden Z2 x Z2 symmetry that protects the scar subspace in the spin-1 XY chain, and simultaneously demonstrate that this protection makes the scars more fragile than the surrounding thermal states, not less.
The scars in the spin-1 XY chain are generated by a spectrum generating algebra — a ladder operator that connects scar states at equally spaced energies, creating a tower of states within the many-body spectrum. The authors show that this tower has the structure of a symmetry-protected trivial phase in a commutant Hamiltonian — a Hamiltonian for which the scar states are ground states and the algebraic structure becomes a manifest symmetry. The hidden Z2 x Z2 symmetry of this commutant Hamiltonian protects the scar subspace against perturbations that respect the symmetry, analogous to how topological phases are protected by their symmetry group.
The Lieb-Schultz-Mattis twist operator provides a diagnostic: applied to scar states, it yields a value of -1, while for ergodic states it approaches zero in the thermodynamic limit. The twist detects the non-trivial character of the scar subspace within the commutant framework, cleanly distinguishing scars from thermal states.
The fragility result is the surprise. Perturbations that break the Z2 x Z2 symmetry destroy the scars more efficiently than they affect the thermal states. The Loschmidt echo — a measure of how much a state changes under perturbation — decays faster for scars than for nearby thermal eigenstates. The Quantum Fisher Information, which measures the sensitivity of a state to parameter changes, is larger for scars. The scars are more responsive to perturbation, not less.
This inverts the naive expectation. Protection suggests robustness — a symmetry-protected phase should be stable against perturbations. And it is, against symmetry-respecting perturbations. But against generic perturbations that break the protecting symmetry, the scars are more vulnerable precisely because they are organized. The thermal states have no structure to disrupt. They are already disordered, already at maximum entropy for their energy. A perturbation that reshuffles their structure doesn't change much because there was no structure to begin with. The scars have structure — the low entanglement, the algebraic tower, the hidden symmetry — and structure is what perturbations destroy.
The tower stands because a symmetry holds. When the symmetry breaks, the tower falls faster than the rubble around it, because the rubble was never standing.