Magic scaling of quantum many-body scar states

Determine whether the magic of the atypical quantum many-body scar eigenstates of the Hamiltonian defined in Eq. (\ref{eq:scar_ham}) scales as O(log N), as conjectured, rather than obeying the volume-law scaling of typical highly excited eigenstates.

Background

The paper studies a periodic spin-chain Hamiltonian hosting quantum many-body scar states that violate the eigenstate thermalization hypothesis. Its numerical results show sharp reductions in the filtered stabilizer Rényi entropy at the scar-state energies, while the thermal Scrooge ensemble describes typical eigenstates but not the scars.

The reported behavior is consistent with an external conjecture that scar-state magic grows only logarithmically with system size, in contrast to the volume-law magic of typical highly excited eigenstates. The precise asymptotic scaling remains unresolved.

References

The dips in the magic of these atypical scar states are consistent with Ref., which conjectures that their magic scales as $O{\log N}$, much smaller than the volume-law scaling of typical highly excited eigenstates.

— Universal equilibrium magic in quantum many-body systems  (2608.22939 - Sarma et al., 24 Aug 2026) in Supplemental Material, Section “Supplementary numerical results,” subsection “Quantum many-body scars”