Multicriticality in stochastic dynamics protected by self-duality

In light of the recent interest in finding multicritical behavior in stochastic systems, we compute the trajectory phase diagram of one-dimensional kinetically constrained models (KCMs), demonstrating the existence of dynamical phases separated by lines of self-duality. We further reveal that multicritical points delimit first-order from continuous active-inactive transition lines. For illustration, we consider four representative KCMs in detail: the domain-wall (DW), Fredrickson-Andersen (FA), the DW East, the ZZZ-FA, and the XOR-FA models. Via exact diagonalization and tensor network methods we achieve three goals: (i) we find that dynamical phases and their transitions can be related by duality arguments in a broad class of KCMs, (ii) we establish the presence of multicritical points on their self-dual lines, and (iii) we intertwine concepts related to dualities of quantum spin systems, classical stochastic dynamics, and large deviation theory.