Enhancing disorder-free localization through dynamically emergent local symmetries

Abstract

Disorder-free localization is a recently discovered phenomenon of nonergodicity that can emerge in quantum many-body systems hosting gauge symmetries when the initial state is prepared in a superposition of gauge superselection sectors. Thermalization is then prevented up to all accessible evolution times despite the model being nonintegrable and translation-invariant. In a recent work [Halimeh, Zhao, Hauke, and Knolle, arXiv:2111.02427], it has been shown that terms linear in the gauge-symmetry generator stabilize disorder-free localization in U(1) gauge theories against gauge errors that couple different superselection sectors. Here, we show in the case of Z2 gauge theories that disorder-free localization can not only be stabilized, but also enhanced by the addition of translationinvariant terms linear in a local Z2 pseudogenerator that acts identically to the full generator in a single superselection sector, but not necessarily outside of it. We show analytically and numerically how this leads through the quantum Zeno effect to the dynamical emergence of a renormalized gauge theory with an enhanced local symmetry, which contains the Z2 gauge symmetry of the ideal model, associated with the Z2 pseudogenerator. The resulting proliferation of superselection sectors due to this dynamically emergent gauge theory creates an effective disorder greater than that in the original model, thereby enhancing disorder-free localization. We demonstrate the experimental feasibility of the Z2 pseudogenerator by providing a detailed readily implementable experimental proposal for the observation of disorder-free localization in a Rydberg setup. CONTENTS

Probing confinement in a $\mathbb{Z}_2$ lattice gauge theory on a quantum computer

“…Outlook.-Our work opens the door to studying a wide range of phenomena in LGTs of coupled matter and gauge fields with discrete symmetries. Ideal target scenarios are, e.g., exotic out-of-equilibrium phenomena such as quantum many-body scars [6] and disorder-free localization [5]. Given the large computational challenges when attempting to connect early-time behavior to latetime dynamics, thermalization of gauge theories is another outstanding question with large relevance, e.g., to high-energy experiments such as heavy-ion collisions [8].…”

“…The necessity of precisely engineering multi-qubit interactions and local constraints is currently imparting a strong momentum onto the field, as it pushes devices beyond their current limits and drives the development of new error mitigation protocols [11-13, 17, 20], such as the one implemented here [10]. Promising proposals exist for generalizing such schemes to more complex situations, including the protection of disorder free localization [5] or non-Abelian gauge theories [11,12,24].…”

“…LGTs have proven to be powerful frameworks to describe the emergence of exotic phenomena also in condensed-matter physics including, e.g., disorder-free localization [5], quantum many-body scars [6], and staircase prethermalization [7]. The rich phenomenology of LGTs is fundamentally linked with local constraints set by the underlying gauge symmetry, which determine the interplay between matter and gauge degrees of freedom.…”

Disorder-free localization transition in a two-dimensional lattice gauge theory

“…LGTs is due to the emergence of so-called gauge superselection sectors, which induce an effective internal quenched disorder for the dynamics. Most models for DFL have been restricted to 1D, where quantum interference induces localization similar to conventional Anderson localization [12][13][14][15][16][17][18]. Recently, certain 2D LGTs have also shown to exhibit localization due to the presence of a non-percolating phase in an emerging classical percolation problem describing the gauge charges [19,20].…”

Fractionalized holes in one-dimensional $\mathbb{Z}_2$ gauge theory coupled to fermion matter -- deconfined dynamics and emergent integrability

“…Here we consider one-component U (1)-symmetric quantum fermion matter hopping on a one-dimensional lattice coupled to dynamical Z 2 gauge fields [27][28][29][30][31][32][33][34][35]. Despite the confining nature of the attractive interaction between lattice fermions mediated by the gauge field, the model is known to form a Luttinger liquid that exhibits gapless deconfined low-energy excitations.…”