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Annihilable Symmetries in Non-Semisimple Models

Updated 7 July 2026
  • Annihilable symmetries are generalized non-invertible symmetry operations whose repeated action nullifies defects, revealing nilpotent and non-semisimple characteristics.
  • They are realized in spin-chain frameworks via the Taft Hopf algebra, where nilpotent operators and projective covers cause distinct quantum states to collapse in the infrared limit.
  • The concept extends to lattice and field-theoretic models through mechanisms like gauging, screening, and condensation, offering insights into symmetry breaking and defect annihilation.

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