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The Kitaev model on the honeycomb lattice is a paradigmatic system known tohost a wealth of nontrivial topological phases and Majorana edge modes. In thestatic case, the Majorana edge modes are nondispersive. When the system isperiodically driven in time, such edge modes can disperse and become chiral. Weobtain the full phase diagram of the driven model as a function of the couplingand the driving period. We characterize the quantum criticality of thedifferent topological phase transitions in both the static and driven model viathe notions of Majorana-Wannier state correlation functions andmomentum-dependent fidelity susceptibilities. We show that the system hostscross-dimensional universality classes: although the static Kitaev model isdefined on a 2D honeycomb lattice, its criticality falls into the universalityclass of 1D linear Dirac models. For the periodically driven Kitaev model,besides the universality class of prototype 2D linear Dirac models, anadditional 1D nodal loop type of criticality exists owing to emergenttime-reversal and mirror symmetries, indicating the possibility of engineeringmultiple universality classes by periodic driving. The manipulation oftime-reversal symmetry allows the periodic driving to control the chirality ofthe Majorana edge states.

Cross-dimensional universality classes in static and periodically driven Kitaev models