Revealing Hidden Symmetries from the Symmetry Projected Spectral
Form Factor

Identifying the symmetry structure of a quantum many-body
system is of great importance in modern condensed matter and high energy
physics. In many systems, only a subset of the true symmetry group is
manifest, leaving hidden symmetries undetected by conventional methods. In this talk, I will introduce the symmetry projected spectral form factor
(SPSFF) as a powerful diagnostic tool for uncovering properties of these
hidden symmetries. I will first discuss the properties of the SPSFF and
formulate the symmetry diagnostic problem as a bootstrap program, including
constraints from branching multiplicity, monoidality, rigidity, and etc.
Then I will provide examples of inferring hidden symmetries in the 1+1 D
lattice models.