Bridging Polynomial and Commutant Methods for Hilbert Space Fragmentation

by Mr Bo-Ting Chen (Princeton)

Tuesday 30 Dec 2025, 14:00 → 15:00 Asia/Taipei

Physics/613 (NTHU)

Hilbert space fragmentation is characterized by the exponential growth in the number of Krylov subspaces with the system size. However, the precise definition of Krylov subspace remains ambiguous. In this talk, I focus on two widely used definitions: the Krylov subspaces based on commutant algebra and those obtained from integer characteristic polynomial factorization. Although these definitions appear to be different, they coincide in many physical systems. I will show that the polynomial-based definition is always finer than the commutant-based one, whenever every generator of the center of the bond algebra has rational eigenvalues. I will further demonstrate that this rational-eigenvalue condition is satisfied in a broad class of models.