Disorder-free localization with Stark gauge protection

Abstract: Disorder-free localization in translation-invariant gauge theories presents a counterintuitive yet powerful framework of ergodicity breaking in quantum many-body physics. The fragility of this phenomenon in the presence of gauge-breaking errors has recently been addressed, but no scheme has been able to reliably stabilize disorder-free localization through all accessible evolution times while preserving the disorder-free property. Here, we introduce the concept of \textit{Stark gauge protection}, which entails a linear sum in gauge-symmetry local (pseudo)generators weighted by a Stark potential. Using exact diagonalization and Krylov-based methods, we show how this scheme can stabilize or even enhance disorder-free localization against gauge-breaking errors in $\mathrm{U}(1)$ and $\mathbb{Z}_2$ gauge theories up to all accessible evolution times, without inducing \textit{bona fide} Stark many-body localization. We show through a Magnus expansion that the dynamics under Stark gauge protection is described by an effective Hamiltonian where gauge-breaking terms are suppressed locally by the protection strength and additionally by the matter site index, which we argue is the main reason behind stabilizing the localization up to all accessible times. Our scheme is readily feasible in modern ultracold-atom experiments and Rydberg-atom setups with optical tweezers.