Disorder-free localization in the Kitaev honeycomb model

Presenting Author: Sayonee Ray, University of New Mexico CQuIC
Contributing Author(s): Adrian Chapman

Philip Anderson's seminal insight is that a quantum particle propagating in a disordered medium is confined, or localized, to a bounded region near its initial position. Recently, this intuition has been challenged by the concept of disorder-free localization, whereby this confinement is dynamically self-induced, even in translationally invariant systems. In this ongoing work, we study how local disturbances propagate in the two-dimensional Kitaev honeycomb model by calculating the infinite temperature out-of-time-ordered correlator (OTOC) for Pauli observables. The Kitaev honeycomb model consists of non-commuting two-body Hamiltonian terms whose ferromagnetic interaction directions are in correspondence with the ''compass" directions of a honeycomb lattice. Surprisingly, this model is exactly solvable, and lies in the same phase as the toric code. We find that our quantity of interest reduces to an average of free-fermion evolution over disordered hopping amplitudes. We therefore observe that Pauli ZZ disturbances reach a localized equilibrium which persists for very long times, and we conjecture that this indeed constitutes a signature of genuine localization. A future direction of this work is to extend our analysis to the finite temperature OTOC and study the effect of temperature on our result.

(Session 5 : Sunday from 5:00pm - 7:00pm)


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