Stability of fragmentation and many-body scars
For a specified constrained spin model, determine which fragmentation or scar diagnostics survive bounded local perturbations preserving its stated exact symmetries, and bound the system-size and perturbation dependence of memory or revival lifetimes.
Problem statement
For a specified constrained spin model, determine which fragmentation or scar diagnostics survive bounded local perturbations preserving its stated exact symmetries, and bound the system-size and perturbation dependence of memory or revival lifetimes.
Lean 4
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Background
Several distinct mechanisms let quantum systems evade the ETH paradigm: integrability (extensively many local conserved charges), many-body localization (emergent l-bits under disorder), Hilbert-space fragmentation (dynamical shattering of the state space into exponentially many disconnected sectors), quantum many-body scars (rare non-thermal eigenstates, as in the PXP/Rydberg model), and pseudolocal or non-Abelian conserved quantities.
What is known: Each mechanism has its own well-developed theory and diagnostic (level statistics, entanglement scaling, revivals, commutant algebras for fragmentation). Recent work (Moudgalya–Motrunich) organizes scars and fragmentation via commutant algebras, a promising unifying language. Integrability is understood via Bethe ansatz / Yang–Baxter structure.
The useful frontier is a stability theorem or counterexample for a fixed mechanism and perturbation class, not the existence of one language for every failure of ETH. Exact fragmentation, long-lived approximate conservation and rare eigenstate scars are distinct. A finite-time revival is not by itself a stable phase; the order of infinite-volume, long-time and vanishing-perturbation limits matters. MBL is treated separately in M4.
Progress & source assessment
Source catalogue review: 4 September 2026. Improved indicates partial progress, including qualified preprint claims.
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