Localization in a random XY model with long-range interactions: Intermediate case between single-particle and many-body problems

Burin, Alexander L.

doi:10.1103/physrevb.92.104428

Cited by 95 publications

(98 citation statements)

References 44 publications

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“…4, red line] [25]. We note that many-body resonance counting suggests a critical power law, α c ¼ 3=2 in one dimension [52], although this delocalization is expected to emerge only for very large systems, and we do not find evidence of such critical delocalization in our simulations.…”

Section: Prl 118 030401 (2017) P H Y S I C a L R E V I E W L E T T Econtrasting

confidence: 35%

“…We emphasize that our proposed realization can likewise be naturally implemented in ultracold polar molecules [46,47] and Rydberg-dressed neutral atom arrays [48,49], both of which also feature long-range interactions. This leads to a key question: can the discrete time crystal survive the presence of such long-range interactions [50][51][52]? To quantitatively probe the effect of the longrange power law and the existence of a DTC phase in trapped ions, we perform a numerical study of U ion with α ¼ 1.5 [53].…”

Section: Prl 118 030401 (2017) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

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How to Create a Time Crystal

Richerme

2017

Physics

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Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry. The period of the resulting discrete time crystal is quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization. Here, we consider a simple model for a onedimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied. We numerically map out its phase diagram and compute the properties of the dynamical phase transition where the time crystal melts into a trivial Floquet insulator. Moreover, we demonstrate that the model can be realized with current experimental technologies and propose a blueprint based upon a one dimensional chain of trapped ions. Using experimental parameters (featuring long-range interactions), we identify the phase boundaries of the ion-time-crystal and propose a measurable signature of the symmetry breaking phase transition. DOI: 10.1103/PhysRevLett.118.030401 Spontaneous symmetry breaking-where a quantum state breaks an underlying symmetry of its parent Hamiltonianrepresents a unifying concept in modern physics [1,2]. Its ubiquity spans from condensed matter and atomic physics to high energy particle physics; indeed, examples of the phenomenon abound in nature: superconductors, Bose-Einstein condensates, (anti)ferromagnets, any crystal, and Higgs mass generation for fundamental particles. This diversity seems to suggest that almost any symmetry can be broken.Spurred by this notion, and the analogy to spatial crystals, Wilczek proposed the intriguing concept of a "time crystal"-a state which spontaneously breaks continuous time translation symmetry [3][4][5]. Subsequent work developed more precise definitions of such time translation symmetry breaking (TTSB) [6][7][8] and ultimately, led to a proof of the "absence of (equilibrium) quantum time crystals" [9]. However, this proof leaves the door open to TTSB in [10,11] has demonstrated that quantum systems subject to periodic driving can indeed exhibit discrete TTSB [10-13]; such systems develop persistent macroscopic oscillations at an integer multiple of the driving period, manifesting in a subharmonic response for physical observables.An important constraint on symmetry breaking in manybody Floquet systems is the need for disorder and localization [10][11][12][13][14][15][16][17]. In the translation-invariant setting, Floquet eigenstates are short-range correlated and resemble infinite temperature states which cannot exhibit symmetry breaking [15,18,19]. Under certain conditions, however, prethermal time-crystal-like dynamics can persist for long times [20,21] even in the absence of localization before ultimately being destroyed by thermalization [17,22].In this Letter, we present three main results. First, by exploring the interplay between entanglement, many body localization and TTSB, we produce a phase diagram for a d...

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Section: Prl 118 030401 (2017) P H Y S I C a L R E V I E W L E T T Econtrasting

confidence: 35%

Section: Prl 118 030401 (2017) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

How to Create a Time Crystal

Richerme

2017

Physics

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“…For this generic situation of J W ij  | | , levels interact in sequence to add Ising terms that cause van der Waals shifts of pairs of dipoles [66]. Figure 6 diagrams an exemplary pairwise interaction of three nearest-neighbour spins i, j and k for the case of L=2.…”

Section: Induced Ising Interactionsmentioning

confidence: 99%

“…Figure 6 diagrams an exemplary pairwise interaction of three nearest-neighbour spins i, j and k for the case of L=2. Spins i and j couple via spin k in a third-order process that proceeds as follows: , , , »  , where J  estimates J ij , for an average value of t ij at an average distance separating spins [66].…”

Section: Induced Ising Interactionsmentioning

confidence: 99%

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Many-body physics with ultracold plasmas: quenched randomness and localization

Sous

Grant

2019

New J. Phys.

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The exploration of large-scale many-body phenomena in quantum materials has produced many important experimental discoveries, including novel states of entanglement, topology and quantum order as found for example in quantum spin ices, topological insulators and semimetals, complex magnets, and high-T c superconductors. Yet, the sheer scale of solid-state systems and the difficulty of exercising exacting control of their quantum mechanical degrees of freedom limit the pace of rational progress in advancing the properties of these and other materials. With extraordinary effort to counteract natural processes of dissipation, precisely engineered ultracold quantum simulators could point the way to exotic new materials. Here, we look instead to the quantum mechanical character of the arrested state formed by a quenched ultracold molecular plasma. This novel class of system arises spontaneously, without a deliberate engineering of interactions, and evolves naturally from statespecified initial conditions, to a long-lived final state of canonical density, in a process that conflicts with classical notions of plasma dissipation and neutral dissociation. We take information from experimental observations to develop a conceptual argument that attempts to explain this state of arrested relaxation in terms of a minimal phenomenological model of randomly interacting dipoles of random energies. This model of the plasma forms a starting point to describe its observed absence of relaxation in terms of many-body localization (MBL). The large number of accessible Rydberg and excitonic states gives rise to an unconventional web of many-body interactions that vastly exceeds the complexity of MBL in a conventional few-level scheme. This experimental platform thus opens an avenue for the coupling of dipoles in disordered environments that will demand the development of new theoretical tools.

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Localization and chaos in a quantum spin glass model in random longitudinal fields: Mapping to the localization problem in a Bethe lattice with a correlated disorder

Burin

2017

Annalen der Physik

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The analytical solution of a many-body localization problem in a quantum Sherrington-Kirkpatrick spin glass model in a random longitudinal field is proposed matching the problem with a model of Anderson localization in a Bethe lattice. The localization transition is dramatically sensitive to the relationship between interspin interaction and random field revealing different regimes in which the interaction can either suppress or enhance the delocalization. The localization is enhanced by decreasing the temperature and the localization transition shows a remarkable universality in a spin glass phase. The observed trends should be qualitatively relevant for other systems showing many-body localization.

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Localization in a random XY model with long-range interactions: Intermediate case between single-particle and many-body problems

Cited by 95 publications

References 44 publications

How to Create a Time Crystal

How to Create a Time Crystal

Many-body physics with ultracold plasmas: quenched randomness and localization

Localization and chaos in a quantum spin glass model in random longitudinal fields: Mapping to the localization problem in a Bethe lattice with a correlated disorder

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