The Quench Action

Caux, Jean-Sébastien

doi:10.1088/1742-5468/2016/06/064006

Cited by 233 publications

(370 citation statements)

References 190 publications

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“…Such ensemble follows from a generalization to periodically driven systems of the generalized Gibbs ensemble, which is believed to describe the asymptotic steady states of quantum-quenched integrable models (for a report on the state of the art, see Refs. [19,20]). Indeed, in quadratic integrable periodically driven systems [16], an extensive number of time-dependent (periodic) conserved quantities I α (t) (with α = 1, .…”

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confidence: 99%

Entanglement entropy in a periodically driven quantum Ising ring

2016

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We numerically study the dynamics of entanglement entropy, induced by an oscillating time periodic driving of the transverse field, h(t), of a one-dimensional quantum Ising ring. We consider several realizations of h(t), and we find a number of results in analogy with entanglement entropy dynamics induced by a sudden quantum quench. After a short-time relaxation, the dynamics of entanglement entropy synchronizes with h(t), displaying an oscillatory behavior at the frequency of the driving. Synchronization in the dynamics of entanglement entropy is spoiled by the appearance of quasirevivals which fade out in the thermodynamic limit, and which we interpret using a quasiparticle picture adapted to periodic drivings. We show that the time-averaged entanglement entropy in the synchronized regime obeys a volume law scaling with the subsystem's size. Such result is reminiscent of a thermal state or a generalized Gibbs ensemble, although the system does not heat up towards infinite temperature as a consequence of the integrability of the model. DOI: 10.1103/PhysRevB.94.134304 The past decade has witnessed a remarkable revival of interest for the nonequilibrium dynamics of quantum manybody systems, mostly triggered by the advances in the experimental control of the tunable coupling, as well as of the environment isolation, of ultracold atomic lattices [1]. The possibility to observe the coherent time-resolved quantum dynamics of many-body systems has stimulated considerable theoretical interest in the different dynamical regimes of many-particle quantum systems, pioneered by studies on quantum quenches [2]. Albeit thermalization is eventually expected in ergodic systems [3], intermediate-time dynamics can display novel features determined by the nature of the driven out of equilibrium dynamics. A paradigmatic example of this scenario is given by periodically driven manybody systems [4], which can be traditionally employed to engineer hopping in optical lattices [5], design artificial gauge fields in cold atoms [6], or more recently to stabilize novel topological states of matter [7]. Such a plethora of promising applications has stimulated a substantial theoretical debate on the properties of many-body dynamics under periodic driving [8]. In the absence of a cooling mechanism, ergodic nonintegrable systems are expected to heat up towards an infinite temperature state [9], as a consequence of resonant energy absorption from the driving. However, even for an isolated periodically driven system, heating can occur on an extremely long time scale, and a richer scenario is expected at the intermediate stages of the dynamics, such as the emergence of novel prethermalized Floquet metastable states [10].At the same time, while entanglement entropy [11] is of key importance in condensed matter to characterize topological phases or to probe nonequilibrium dynamics [12], few works have addressed so far the evolution and the scaling of entanglement entropy in periodically driven quantum many-body systems [13]. In contrast, for a q...

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Entanglement entropy in a periodically driven quantum Ising ring

2016

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“…In terms of the densities of sine-Gordon physical particles and magnons, obtained from (34,35,36), this becomes…”

Section: From the Operators X J (α) To The String Densitiesmentioning

confidence: 99%

Quasilocal charges and progress towards the complete GGE for field theories with nondiagonal scattering

Vernier¹,

Cubero²

2017

J. Stat. Mech.

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It has recently been shown that some integrable spin chains possess a set of quasilocal conserved charges, with the classic example being the spin-1 2 XXZ Heisenberg chain. These charges have been proven to be essential for properly describing stationary states after a quantum quench, and must be included in the generalized Gibbs ensemble (GGE). We find that similar charges are also necessary for the GGE description of integrable quantum field theories with non-diagonal scattering. A stationary state in a non-diagonal scattering theory is completely specified by fixing the mode-occupation density distributions of physical particles, as well auxiliary particles which carry no energy or momentum. We show that the set of conserved charges with integer Lorentz spin, related to the integrability of the model, are unable to fix the distributions of these auxiliary particles, since these charges can only fix kinematical properties of physical particles. The field theory analogs of quasilocal lattice charges are therefore necessary. As a concrete example, we find the complete set of charges needed in the sine-Gordon model, by using the fact that this field theory is recovered as the continuum limit of a spatially inhomogeneous version of the XXZ chain. The set of quasilocal charges of the lattice theory are shown to become a set local charges with fractional spin in the field theory.

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“…This was done for the entire range of attractive interactions in the thermodynamic limit 1 [9,10] using the quench-action method [202,203]. Within this approach, the relaxed value of certain observables can be calculated in a single representative eigenstate of the system.…”

Section: Introductionmentioning

confidence: 99%

“…[202] conjectured that the dynamics and relaxed value of certain local observables following an interaction strength quench are captured by a representative eigenstate of the postquench Hamiltonian and excitations around it -the so-called quench action approach [203]. The method was introduced for integrable models with Bethe ansatz solution, Refs.…”

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“…Its value for non-equilibrium dynamics comes from a numerically convenient determinant expression for so-called form-factors [208], which are matrix elements of physical operators. As for the quench action method, the representation of the initial state in the eigenstates of the Hamiltonian governing the time-evolution is needed and is only known for some specific 20 Although it is in principle not restricted to those [203].…”

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Nonequilibrium dynamics of a one-dimensional Bose gas via the coordinate Bethe ansatz

Zill¹

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This thesis is concerned with non-equilibrium phenomena in interacting quantum manybody systems. Specifically, we investigate the time-evolution and relaxation dynamics of Bose gases in a highly restricted geometry, which constrains the dynamics to one spatial dimension. This leads to a description of the system in terms of a simple model Hamiltonian which permits exact many-body quantum mechanical solutions due to its integrability.In the first part of this thesis, a computational method is developed to obtain experimentally relevant correlation functions in the framework of the coordinate Bethe ansatz.We employ this method to compute exact ground-state correlation functions of the LiebLiniger gas for up to seven particles covering the whole regime of repulsive interactions. We also investigate the dynamics of the system after an instantaneous change of the interaction strength. This quantum quench deposits large amounts of energy that cannot be dissipated due to the system being closed, and so the dynamics far from equilibrium are probed. We prepare the system in two different initial states, and quench to the same final interaction strength. The latter is determined in such a way that the added energy due to the quench is the same for both scenarios. Conventional statistical mechanics predicts the same relaxed state, but due to the integrability of the system all considered correlation functions of the relaxed states differ from each other and also from the thermal ones.We then investigate the dynamics and relaxed state for a quench from zero to repulsive interactions in more detail, focussing on the mechanism of relaxation and the involved time-scales. We find that local correlation functions relax on time-scales determined by the interaction strength, in contrast to non-local correlation functions, whose relaxation time-scale is proportional to the system size.Next, we employ the same methodology to study the one-dimensional Bose gas with attractive interactions. In this case many-body bound states are permissible solutions of the Lieb-Liniger model. We compare exact ground-state correlation functions of up to seven particles to their corresponding mean-field solution. The latter displays a quantum phase transition at a critical interaction strength, marking the transition from a uniformdensity state to a localized bright soliton. Our exact results agree remarkably well with the corresponding mean-field solution past the critical point. We also investigate the dynamics following an interaction strength quench, starting again from the non-interacting ground state. Bound states strongly influence correlation functions for all post-quench interaction strengths, and local correlation functions are largely increased compared to their initial value.In the last part of this thesis, we investigate the behavior of the one-dimensional Bose gas under periodic driving of the interaction strength. To this end, we extend the coordinate Bethe-ansatz formalism by employing Floquet theory to obtain solutions for the...

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The Quench Action

Cited by 233 publications

References 190 publications

Entanglement entropy in a periodically driven quantum Ising ring

Entanglement entropy in a periodically driven quantum Ising ring

Quasilocal charges and progress towards the complete GGE for field theories with nondiagonal scattering

Nonequilibrium dynamics of a one-dimensional Bose gas via the coordinate Bethe ansatz

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