Destruction of string order after a quantum quench

Strinati, Marcello Calvanese; Mazza, Leonardo; Endres, Manuel; Rossini, Davide; Fazio, Rosario

doi:10.1103/physrevb.94.024302

Cited by 16 publications

(6 citation statements)

References 53 publications

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“…Using our individual addressing laser, we could generate controllable terms of the form αS z i + β(S z i ) 2 in order to engineer a disordered S = 1 chain. This provides a toolbox for S = 1 quantum simulations as complete as that for S = 1/2, and opens the door to experiments studying localization in integer spin chains [94,95].…”

Section: Discussionmentioning

confidence: 99%

Non-thermalization in trapped atomic ion spin chains

Hess¹,

Becker²,

Kaplan³

et al. 2017

Phil. Trans. R. Soc. A.

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Linear arrays of trapped and laser-cooled atomic ions are a versatile platform for studying strongly interacting many-body quantum systems. Effective spins are encoded in long-lived electronic levels of each ion and made to interact through laser-mediated optical dipole forces. The advantages of experiments with cold trapped ions, including high spatio-temporal resolution, decoupling from the external environment and control over the system Hamiltonian, are used to measure quantum effects not always accessible in natural condensed matter samples. In this review, we highlight recent work using trapped ions to explore a variety of non-ergodic phenomena in long-range interacting spin models, effects that are heralded by the memory of out-of-equilibrium initial conditions. We observe long-lived memory in static magnetizations for quenched many-body localization and prethermalization, while memory is preserved in the periodic oscillations of a driven discrete time crystal state.This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.

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Section: Discussionmentioning

confidence: 99%

Non-thermalization in trapped atomic ion spin chains

Hess¹,

Becker²,

Kaplan³

et al. 2017

Phil. Trans. R. Soc. A.

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“…More precisely we examine the time evolution of the string order parameter (SOP) in the S = 1 XXZ model. Although this model has been investigated before regarding the thermalization of string order [24,25], we point out that its dynamics is much richer and there is a so far unrecognized connection between the dynamics of the SOP and the underlying DQPTs, which have also not been observed before. More precisely, we consider several types of quenches and demonstrate that if a DQPT occurs during the time evolution, then it is accompanied by the zero of one of the SOPs.…”

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confidence: 82%

Dynamical Topological Quantum Phase Transitions in Nonintegrable Models

et al. 2019

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We consider sudden quenches across quantum phase transitions in the S = 1 XXZ model starting from the Haldane phase. We demonstrate that dynamical phase transitions may occur during these quenches that are identified by nonanalyticities in the rate function for the return probability. In addition, we show that the temporal behavior of the string order parameter is intimately related to the subsequent dynamical phase transitions. We furthermore find that the dynamical quantum phase transitions can be accompanied by enhanced two-site entanglement.Introduction.-Nonequilibrium dynamics of manybody quantum systems under unitary time evolution continue to pose a challenging problem. The time evolution of a quantum system after a sudden global quench plays a distinguished role in this field since this process can be routinely carried out in experiments and it is addressable in theoretical calculations [1].The quench process is even more interesting when it drives the system through an equilibrium phase transition. This has opened up a new area of research named dynamical quantum phase transitions (DQPTs) [2][3][4]. Although they are not in one-to-one correspondence with the equilibrium phase transitions, but rather a new form of critical behavior, they often emerge when the quench crosses a phase transition. Recently, direct experimental observation of DQPTs has been reported, where a transverse-field Ising model was realized with trapped ions [5,6]. For the better understanding of DQPTs several integrable models have been considered [4,[7][8][9][10][11], where the time evolution can be solved exactly. It has been revealed that, like equilibrium phase transitions, DQPTs also affect other observables. For example, when the quench starts from a broken-symmetry phase, where the order can be characterized by a local order parameter, the order parameter exhibits a temporal decay with a series of times where it vanishes [4,12]. These times usually coincide with the times where the DQPTs occur. The case is more difficult when one considers a nonintegrable model [13][14][15][16][17][18]. Namely, the obvious choice of an observable (e.g. the equilibrium order parameter) may not follow the dynamics dictated by the DQPTs and the connection between them remains elusive like in the case of a nonintegrable Ising chain [19] or Bose-Hubbard model [20]. Thus, the relation of DQPTs to observables in nonintegrable models deserves further investigation in general.In this work we study quenches starting from the Haldane phase to regimes where the ground state has trivial topology. The Haldane phase is a paradigmatic exam-

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“…More recently, the topological properties of quantum states far from equilibrium have been examined [9][10][11][12][13][14][15][16][17][18][19][20][21], motivated by possibilities to study coherent dynamics in cold atom experiments [22][23][24]. The Chern number after a quantum quench has been shown to be constant in time [15][16][17][18], a result that has often been assumed to be a universal feature of all bulk invariants in noninteracting fermionic systems [19,21].…”

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confidence: 99%

Topology of One-Dimensional Quantum Systems Out of Equilibrium

2018

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We study the topological properties of one-dimensional systems undergoing unitary time evolution. We show that symmetries possessed both by the initial wave function and by the Hamiltonian at all times may not be present in the time-dependent wave function-a phenomenon which we dub "dynamically induced symmetry breaking." This leads to the possibility of a time-varying bulk index after quenching within noninteracting gapped topological phases. The consequences are observable experimentally through particle transport measurements. With reference to the entanglement spectrum, we explain how the topology of the wave function can change out of equilibrium, both for noninteracting fermions and for symmetry-protected topological phases protected by antiunitary symmetries.

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Destruction of string order after a quantum quench

Cited by 16 publications

References 53 publications

Non-thermalization in trapped atomic ion spin chains

Non-thermalization in trapped atomic ion spin chains

Dynamical Topological Quantum Phase Transitions in Nonintegrable Models

Topology of One-Dimensional Quantum Systems Out of Equilibrium

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