Strong zero modes in chiral Z₃ clock models

The strong zero mode in Z₃ clock models, unlike the Z₂ models, is expected not to exist throughout the phase diagram even when there are weak edge modes that switch the system between the symmetry-breaking ground states. The strong mode stability in Z₃ models away from fine-tuned parameters is yet to be fully characterized. In this work, we investigate the zero-energy edge mode stability and dynamics in the chiral clock model away from the fine-tuned parameters. We show aspects of the predicted stability and map the strong zero mode to the topological edge mode of an SSH-like model through recently developed operator Krylov techniques. Adding interactions, we discuss how the strong mode becomes a long-lived almost strong mode, again using the language of edge state tunneling within the Krylov operator Hamiltonian.