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Center for Nonlinear Studies |
Recently, Phil Anderson's seminal insight about localization in the presence of disorder has been challenged by the concept of disorder-free localization, whereby particle localization is dynamically self-induced, even in translationally invariant systems. We study how quench errors propagate in the two dimensional Kitaev honeycomb model (KHM). Even though the behavior of this model is qualitatively similar to that of the toric code in most regimes, certain interesting effects in the low-temperature, finite size regime were observed. A preferred lattice direction for error propagation was observed and anyon diffusion was found to be geometrically constrained, as was found by Lee et al.(2017). We support this observation by calculating the infinite temperature out-of-time-ordered correlator (OTOC) of Pauli errors in the 1D analogue of the model (decoupled chains with only $XX$ and $YY$ interaction terms). In the 2D KHM, we observe localization-like behaviour of Pauli $ZZ$ errors, where even at long enough time scales, the magnitude of the OTOC reduces to only half of the peak value at the initial point and remains localized over a localization length. The $ZZ$ operators grow like path operators with pairs of fermions localised at the endpoints and can be shown to be an invariant of this model. We define an operator $\Lambda_s$, which is the sum of such paths between all pairs of initial and final points, in a given vortex configuration sector, and show that it commutes with two copies of the Hamiltonian. For a given pair of initial and final points, any connecting path is equal to any other connecting path upto a sign which is given by the parity of the plaquette operators enclosed by the paths.
Host: Yigit Subasi