Robust and robuster: Towards absolutely stable ergodicity breaking: Part II

Hilbert-space shattering is usually presented as a delicate phenomenon, wherein generic perturbations quickly restore ergodicity. The recently constructed group-based quantum loop models robustly break ergodicity even in the presence of generic perturbations, at least for timescales exponentially long in inverse perturbation strength. In this talk, we argue that in some group-based models, within a region of parameter space, each Krylov sector hosts a lowest-energy state that remains absolutely stable to generic perturbations for times that diverge with system size. We also discuss how the conjectured absolute stability depends on the input group. In three dimensions we argue that this ergodicity breaking even survives coupling to a nonzero-temperature heat bath.