Classification of SL(2) deformed Floquet conformal field theories and holography

Classification of the non-equilibrium many-body dynamics is a challenging problem in condensed matter physics and statistical mechanics. In this seminar, I talk about the basic question that whether a (1+1) dimensional conformal field theory is stable or not under a periodic driving with N non-commuting Hamiltonians. Previous work showed that a Floquet CFT with certain SL(2) deformed Hamiltonians exhibit both non-heating (stable) and heating (unstable) phases. In this talk, I show that the phase diagram depends on the concrete types of the driving Hamiltonians. In general, the heating phase is generic, but the non-heating phase may be absent in the phase diagram. For the existence of the non-heating phases, we give sufficient and necessary conditions. The results also apply to the single quantum quench problem with N=1. Relations to holography will be briefly discussed.