Anyonic self-induced disorder in a stabilizer code: Quasi many-body localization in a translational invariant model

Abstract

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...

Emergent statistical bubble localization in aZ2lattice gauge theory

“…Indeed, the matter degrees of freedom in the single particle limit λ = 0 (equivalent to topologically trivial regime of the spin subsystem) are totally extended. Therefore, in stark contrast to the previous studies on disorder-free localization 35,36,38,63 and quasi-MBL in transnational invariant systems [31][32][33][34] , here, in the limit of vanishing interaction, the matter dynamics is not adiabatically connected to an effective single-particle localized model. Hence, our proposed setting for interaction-driven self-localization is possibly the minimal (gauge) model dropping all prior expectation regarding cMBL.…”

“…In spite of their eventual thermalization, in the intermediate time scales they look like true MBL, hence the name "quasi-MBL" 33 . Such dynamical localization yet with topological non-trivial character is also reported in a self-correcting memory, with the mutual braiding statistics as the origin of the emergent disorder 34 . A closely related concept also concerns the coexistence of disentangled localized and ergodic degrees of freedom in multi-component systems which brings about the idea of quantum disentangled liquid (QDL) 39,40 ; a thermal state of matter whose hidden locality can be uncovered through a projective local measurement of different constituting species.…”

“…Recently, the presumed necessity of the outlined ingredients for the presence of localization is a subject of ongoing debate [27][28][29][30][31][32][33][34][35][36][37][38] . A fresh perspective proposed an emergent dynamical glassiness, initiated in an inhomogeneous state, which is realizable in translational invariant models consisting of massimbalanced (quasi-) particles [31][32][33][34] . In spite of their eventual thermalization, in the intermediate time scales they look like true MBL, hence the name "quasi-MBL" 33 .…”

Aspects of non-equilibrium in classical and quantum systems: Slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics

“…A key distinction between MBL and classical glasses is that the former are disordered systems while in the latter disorder is absent. Whether MBL can exist in translationally invariant systems is still debated [96,71,97,98,99,100,101,102,103,104]. Even if it were the case that strict asymptotic quantum non-ergodicity could not exist in the absence of disorder, an interesting question to address is whether the standard mechanisms for glassy slowing down -in particular kinetic constraints encoding steric restrictions to local motion -can give rise to analogous slow relaxation in closed quantum systems.…”

Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations

“…21,22 Similar type of physics has recently been explored in quantum systems where a "quasi many-body localized" behavior was proposed to occur in the absence of disorder. [23][24][25][26][27][28][29][30][31][32][33][34][35] Recently, a striking phenomenon suggestive of a different mechanism of weak ergodicity breaking was discovered experimentally. 36 A Rydberg atoms platform [36][37][38] was used to realize a quantum model with kinetic constraints induced by strong nearest-neighbour repulsion between atoms in excited states.…”