Absence of localization in interacting spin chains with a discrete symmetry

In this talk, I will present a proof of delocalization in spin chains symmetric under a combination of mirror and spin-flip symmetries and with a nondegenerate spectrum. The proof applies to two prominent examples: the Stark many-body localization system (Stark-MBL) and the symmetrized many-body localization system (symmetrized–MBL). I will also provide numerical evidence of delocalization at all energy densities in these models and show that the delocalization mechanism appears robust to weak symmetry breaking.