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Almost strong edge-mode operators arising at the boundaries of certaininteracting 1D symmetry protected topological phases with \(Z_2\) symmetry haveinfinite temperature lifetimes that are non-perturbatively long in theintegrability breaking terms, making them promising as bits for quantuminformation processing. We extract the lifetime of these edge-mode operatorsfor small system sizes as well as in the thermodynamic limit. For the latter, aLanczos scheme is employed to map the operator dynamics to a one dimensionaltight-binding model of a single particle in Krylov space. We find this model tobe that of a spatially inhomogeneous Su-Schrieffer-Heeger model with a hoppingamplitude that increases away from the boundary, and a dimerization thatdecreases away from the boundary. We associate this dimerized or staggeredstructure with the existence of the almost strong mode. Thus the short timedynamics of the almost strong mode is that of the edge-mode of theSu-Schrieffer-Heeger model, while the long time dynamics involves decay due totunneling out of that mode, followed by chaotic operator spreading. We alsoshow that competing scattering processes can lead to interference effects thatcan significantly enhance the lifetime.

Lifetime of almost strong edge-mode operators in one dimensional, interacting, symmetry protected topological phases