We enquire into the quasi-many-body localization in topologically ordered states of matter, revolving around the case of Kitaev toric code on the ladder geometry, where different types of anyonic defects carry different masses induced by environmental errors. Our study verifies that the presence of anyons generates a complex energy landscape solely through braiding statistics, which suffices to suppress the diffusion of defects in such clean, multi-component anyonic liquid. This non-ergodic dynamics suggests a promising scenario for investigation of quasi-many-body localization. Computing standard diagnostics evidences that a typical initial inhomogeneity of anyons gives birth to a glassy dynamics with an exponentially diverging time scale of the full relaxation. Our results unveil how self-generated disorder ameliorates the vulnerability of topological order away from equilibrium. This setting provides a new platform which paves the way toward impeding logical errors by self-localization of anyons in a generic, high energy state, originated exclusively in their exotic statistics. Many-body localization (MBL) [1][2][3][4][5][6] generalizes the concept of single particle localization [7] to isolated interacting systems, where many-body eigenstates in the presence of sufficiently strong disorder can be localized in a region of Hilbert space even at nonzero temperature. An MBL system comes along with universal characteristic properties such as area-law entanglement of highly excited states (HES) [5,8], power-law decay and revival of local observables [9,10], logarithmic growth of entanglement [11][12][13][14] as well as the violation of "eigenstates thermalization hypothesis" (ETH) [15][16][17]. The latter raises the appealing prospect of protecting quantum order as well as storing and manipulating coherent information in out-of-equilibrium many-body states [18][19][20][21][22].Recently it has been questioned [23-32] whether quench disorder is essential to trigger ergodicity breaking or one might observe glassy dynamics in translationally invariant systems, too. In such models initial random arrangement of particles effectively fosters strong tendency toward selflocalization characterized by MBL-like entanglement dynamics, exponentially slow relaxation of a typical initial inhomogeneity and arrival of inevitable thermalization. This asymptotic MBL-tagged quasi-MBL [30]-in contrast to the genuine ones, is not necessarily accompanied by the emergence of infinite number of conserved quantities [33][34][35][36].Here we present a novel mechanism toward quasi-MBL in a family of clean self-correcting memories, in particular the Kitaev toric code [37,38] on ladder geometry, a.k.a. the Kitaev ladder (KL) [39,40]. The elementary excitations of KL are associated with point-like quasi-particles, known as electric (e) and magnetic (m) charges. Our main interest has its roots in the role of non-trivial statistics between anyons that naturally live in (highly) excited states of such models.Stable topological memories, by definiti...

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We show that the rainbow state, which has volume law entanglement entropy for most choices of bipartitions, can be embedded in a many-body localized spectrum. For a broad range of disorder strengths in the resulting model, we numerically find a narrow window of highly entangled states in the spectrum, embedded in a sea of area law entangled states. The construction hence embeds mobility edges in many-body localized systems. This can be thought of as the complement to manybody scars, an 'inverted quantum many-body scar', providing a further type of setting where the eigenstate thermalization hypothesis is violated.

We introduce a clean cluster spin chain coupled to fully interacting spinless fermions, forming an unconstrained Z2 lattice gauge theory (LGT) which possesses dynamical proximity effect controlled by the entanglement structure of the initial state. We expand the machinery of interaction-driven localization to the realm of LGTs such that for any starting product state, the matter fields exhibits emergent statistical bubble localization, which is driven solely by the cluster interaction, having no topologically trivial non-interacting counterpart, and thus is of a pure dynamical many-body effect. In this vein, our proposed setting provides possibly the minimal model dropping all the conventional assumptions regarding the existence of many-body localization. Through projective measurement of local constituting species, we also identify the coexistence of the disentangled nonergodic matter and thermalized gauge degrees of freedom which stands completely beyond the standard established phenomenology of quantum disentangled liquids. As a by product of self-localization of the proximate fermions, the spin subsystem hosts the long-lived topological edge zero modes, which are dynamically decoupled from the thermalized background Z2 charges of the bulk, and hence remains cold at arbitrary highenergy density. This provides a convenient platform for strong protection of the quantum bits of information which are embedded at the edges of completely ergodic sub-system; the phenomenon that in the absence of such proximity-induced self-localization could, at best, come about with a pre-thermal manner in translational invariant systems. Finally, by breaking local Z2 symmetry of the model, we argue that such admixture of particles no longer remains disentangled and the ergodic gauge degrees of freedom act as a "small bath" coupled to the localized components. arXiv:1810.08434v2 [cond-mat.str-el]

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