Slow dynamics in translation-invariant quantum lattice models

Michailidis, Alexios A.; Žnidarič, Marko; Medvedyeva, M. V.; Abanin, Dmitry A.; Prosen, Tomaž; Papić, Zlatko

doi:10.1103/physrevb.97.104307

Cited by 46 publications

(37 citation statements)

References 41 publications

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“…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.…”

Section: B Dynamical Localization Controlled By the Entanglement Strcontrasting

confidence: 63%

Emergent statistical bubble localization in aZ2lattice gauge theory

2019

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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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Section: B Dynamical Localization Controlled By the Entanglement Strcontrasting

confidence: 63%

Emergent statistical bubble localization in aZ2lattice gauge theory

2019

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“…Furthermore, when looking carefully at the lower panel of Fig. 3, we observe a non-monotonic dependence of the exponents; the dynamics starts slowing down and then accelerates with increasing time, for a fixed Γ, seen as an upturn of α at longer time and at larger L. This suggests that the slow dynamics might be a transient phenomena (as also observed in certain translationally invariant lattice models [50]).…”

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confidence: 50%

Apparent slow dynamics in the ergodic phase of a driven many-body localized system without extensive conserved quantities

2019

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We numerically study the dynamics on the ergodic side of the many-body localization transition in a periodically driven Floquet model with no global conservation laws. We describe and employ a numerical technique based on the fast Walsh-Hadamard transform that allows us to perform an exact time evolution for large systems and long times. As in models with conserved quantities (e.g., energy and/or particle number) we observe a slowing down of the dynamics as the transition into the many-body localized phase is approached. More specifically, our data is consistent with a subballistic spread of entanglement and a stretched-exponential decay of an autocorrelation function, with their associated exponents reflecting slow dynamics near the transition for a fixed system size. However, with access to larger system sizes, we observe a clear flow of the exponents towards faster dynamics and can not rule out that the slow dynamics is a finite-size effect. Furthermore, we observe examples of non-monotonic dependence of the exponents with time, with dynamics initially slowing down but accelerating again at even larger times, consistent with the slow dynamics being a crossover phenomena with a localized critical point.

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“…19 For simplicity, we focus on initial states that are product states of atoms compatible with the Rydberg constraint (recent work in Ref. 58 studied the revivals from more general classes of weaklyentangled initial states). One such initial state is the Néel state |ψ(0) = |Z 2 ≡ |0101... , which gives rise to revivals in the quantum fidelity,…”

Section: A Brief Overview Of Pxp Modelmentioning

confidence: 99%

Quantum scars as embeddings of weakly broken Lie algebra representations

2020

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We present an interpretation of scar states and quantum revivals as weakly "broken" representations of Lie algebras spanned by a subset of eigenstates of a many-body quantum system. We show that the PXP model, describing strongly-interacting Rydberg atoms, supports a "loose" embedding of multiple su(2) Lie algebras corresponding to distinct families of scarred eigenstates. Moreover, we demonstrate that these embeddings can be made progressively more accurate via an iterative process which results in optimal perturbations that stabilize revivals from arbitrary charge density wave product states, |Zn , including ones that show no revivals in the unperturbed PXP model. We discuss the relation between the loose embeddings of Lie algebras present in the PXP model and recent exact constructions of scarred states in related models. arXiv:2001.08232v1 [cond-mat.str-el]

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Slow dynamics in translation-invariant quantum lattice models

Cited by 46 publications

References 41 publications

Emergent statistical bubble localization in aZ2lattice gauge theory

Emergent statistical bubble localization in aZ2lattice gauge theory

Apparent slow dynamics in the ergodic phase of a driven many-body localized system without extensive conserved quantities

Quantum scars as embeddings of weakly broken Lie algebra representations

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