Perturbatively Stable Self-Correcting Classical Memory from Gauge Averaging

Abstract

We show that the self-correcting memory in 3d Wegner gauge theory is stable to arbitrary small enough perturbations of the Hamiltonian. Our proof relies on a new method we dub ``gauge averaging'', which gives conditions under which explicitly broken gauge symmetries are effectively restored by fluctuations. These conditions show that the self-correcting memory phase is fluctuation stabilized, with its robustness to perturbations increasing with increasing temperature, up to some $T_c>0$.

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