Disorder-free localization in the Kitaev Honeycomb Model

We study operator propagation and scrambling in the two-dimensional Kitaev honeycomb model. An exact solution for this model allows us to calculate the infinite-temperature out-of-time-ordered correlator for Pauli observables, where we find that the infinite-temperature average over gauge sectors manifests as a disorder average for this quantity. This induces a localization effect for observables in the bond algebra of the Hamiltonian, while observables outside of the algebra completely scramble. We interpret our result in terms of the diffusion of Pauli strings, whose endpoints are localized yet whose interiors propagate freely. We further find that, in the ground state gauge sector of the model, operators do not localize. We further extend our analysis to the finite temperature regime using Monte Carlo Metropolis-Hastings methods.