Nonequilibrium quantum phase transitions in the Ising model

Bastidas, V. M.; Emary, Clive; Schaller, Gernot; Brandes, Tobias

doi:10.1103/physreva.86.063627

Cited by 70 publications

(84 citation statements)

References 47 publications

(130 reference statements)

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“…Here, very different fundamental aspects can be mentioned, including photo-induced biological processes [1, 2], formation of strongly-correlated bound-states [3,4], quantum phase transitions [5][6][7], relaxation and equilibration dynamics [8][9][10]. Among all, the recent technological developments in atomic and condensed matter physics offer a very promising platform to investigate these important issues.…”

Section: Introductionmentioning

confidence: 99%

Quench-induced entanglement and relaxation dynamics in Luttinger liquids

et al. 2017

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We investigate the time evolution towards the asymptotic steady state of a one dimensional interacting system after a quantum quench. We show that at finite times the latter induces entanglement between right-and left-moving density excitations, encoded in their cross-correlators, which vanishes in the long-time limit. This behavior results in a universal time-decay ∝ t −2 of the system spectral properties, in addition to non-universal power-law contributions typical of Luttinger liquids. Importantly, we argue that the presence of quench-induced entanglement clearly emerges in transport properties, such as charge and energy currents injected in the system from a biased probe, and determines their long-time dynamics. In particular, the energy fractionalization phenomenon turns out to be a promising platform to observe the universal power-law decay ∝ t −2 induced by entanglement and represents a novel way to study the corresponding relaxation mechanism.

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Section: Introductionmentioning

confidence: 99%

Quench-induced entanglement and relaxation dynamics in Luttinger liquids

et al. 2017

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“…This model shows a series of interesting Floquet resonances [6,68]. They are discussed in detail in Ref.…”

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confidence: 99%

“…(see Refs. [6,31,32,63,64,68,[89][90][91] for details). After a Fourier transform, the Hamiltonian can be decomposed in L/2 2 × 2 blocks of the formĤ …”

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confidence: 99%

Kibble-Zurek scaling in periodically driven quantum systems

Russomanno¹,

Torre²

2016

EPL

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-We study the slow crossing of non-equilibrium quantum phase transitions in periodically-driven systems. We explicitly consider a spin chain with a uniform time-dependent magnetic field and focus on the Floquet state that is adiabatically connected to the ground state of the static model. We find that this Floquet ground state undergoes a series of quantum phase transitions characterized by a non-trivial topology. To dynamically probe these transitions, we propose to start with a large driving frequency and slowly decrease it as a function of time. Combining analytical and numerical methods, we uncover a Kibble-Zurek scaling that persists in the presence of moderate interactions. This scaling can be used to experimentally demonstrate non-equilibrium transitions that cannot be otherwise observed.Recent experiments on artificial quantum many-body systems demonstrated quantum-coherent evolution under various external perturbations [1,[1][2][3][4] and triggered the study of fundamental aspects of quantum non-equilibrium physics. One important direction is the quest for universal properties in the dynamics [4][5][6][7][8][9][10][11]. A universal non-equilibrium behaviour can originate from the universality of an underlying equilibrium problem [5,6]: A well known example is offered by the Kibble-Zurek (K-Z) scaling observed when crossing a quantum phase transition [4,7,[12][13][14]. In addition, recent studies found evidence of genuine non-equilibrium universality following a quantum quench [8][9][10][11], or in presence of a timedependent noise [15,16]. Another important direction is the exploration of the conditions for an asymptotic steady state [4,. In the context of quantum quenches, it was found that systems with a continuous spectrum generically relax to a diagonal ensemble [37,38]. Current investigations focus on understanding when this asymptotic condition is thermal (ergodic dynamics) and when it is not (regular dynamics) [20,21,[23][24][25]39]. The transition from regular to ergodic dynamics is connected to the emergence of quantum chaos [41][42][43] and to the many-body localization/delocalization transition [24,25,39,[44][45][46][47][48]. These studies are deeply related to the main problem of statistical mechanics: how microscopic quantum coherent dynamics can induce macroscopic thermalization [20,39,49,50].In this work we address the universal scaling and the absence of thermalization in periodically-driven many-body systems . We focus on Floquet states, the eigenstates of the periodically driven dynamics. We specifically address a Floquet state which shows many properties analogous to the ground state in the static system: we term "Floquet ground state" (FGS). We emphasize that -opposite to the GS of a static Hamiltonian -the FGS depends on time in a periodic fashion (up to a phase factor) and, in general, cannot be found as the minimum-energy eigenstate of any Hamiltonian. Nevertheless it shows many properties similar to the GS of a static Hamiltonian. First of all, it shows an area-law entan...

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“…The interest in periodically driven systems -a long-standing topic in quantum chaos of small quantum systems [22] -has risen again vigorously only quite recently, with a focus on many-body dynamics [23][24][25][26][27][28][29][30][31] and its properties of stability and ergodicity [32]. In a recent work [23] it was proposed that a periodically driven closed quantum system might display, in the thermodynamic limit, a tendency towards a fully coherent "periodic steady state" -a kind of diagonal ensemble [6,16] for periodically driven systems -, where destructive interference effects average to zero for long times the transient fluctuations induced by offdiagonal Floquet matrix elements.…”

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Thermalization in a periodically driven fully connected quantum Ising ferromagnet

Russomanno¹,

Fazio²,

Santoro³

2015

EPL

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-By means of a Floquet analysis, we study the quantum dynamics of a fully connected Lipkin-Ising ferromagnet in a periodically driven transverse field showing that thermalization in the steady state is intimately connected to properties of the N → ∞ classical Hamiltonian dynamics. When the dynamics is ergodic, the Floquet spectrum obeys a Wigner-Dyson statistics and the system satisfies the eigenstate thermalization hypothesis (ETH): Independently of the initial state, local observables relax to the T = ∞ thermal value, and Floquet states are delocalized in the Hilbert space. On the contrary, if the classical dynamics is regular no thermalization occurs. We further discuss the relationship between ergodicity and dynamical phase transitions, and the relevance of our results to other fully-connected periodically driven models (like the BoseHubbard), and possibilities of experimental realization in the case of two coupled BEC.Introduction. Recent experimental advances in ultracold atomic systems [1-4] and femtosecond resolved spectroscopies [5] have made the study of out-of-equilibrium closed many-body quantum systems no longer a purely academic question. The key problem in this context are the properties of the final/steady state after the system has undergone a time-dependent perturbation [6,7]. Depending on the nature of the perturbation, particular aspects acquire a prominent role. For a gentle (quasiadiabatic) driving, the distance of the evolved final state from the instantaneous ground state carries precious information on the crossing of quantum critical points [8] and on the accuracy of quantum adiabatic computation [9] and quantum annealing protocols [10][11][12]. In the opposite case of a sudden quench, the focus is on the (possible) thermal properties of the steady state. Thermalization is expected in "classically ergodic" systems, where the Hamiltonian behaves as a random matrix [13], its eigenstates obey the eigenstate thermalization hypothesis (ETH) [6,[14][15][16], and relaxation to the micro-canonical ensemble, with vanishing fluctuations in the thermodynamic limit, follows.

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Nonequilibrium quantum phase transitions in the Ising model

Cited by 70 publications

References 47 publications

Quench-induced entanglement and relaxation dynamics in Luttinger liquids

Quench-induced entanglement and relaxation dynamics in Luttinger liquids

Kibble-Zurek scaling in periodically driven quantum systems

Thermalization in a periodically driven fully connected quantum Ising ferromagnet

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