Quantum quench in interacting field theory: A self-consistent approximation

Sotiriadis, Spyros; Cardy, John

doi:10.1103/physrevb.81.134305

Cited by 132 publications

(255 citation statements)

References 43 publications

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“…There are two classes of quenches; global quenches and local quenches. The global quenches are triggered by changing parameters homogeneously, e.g., [40][41][42][43]. When parameters are changed homogeneously, we are able to study the thermalization of a subsystem and its thermalization time by measuring its entanglement entropy.…”

Section: Contentsmentioning

confidence: 99%

Notes on quantum entanglement of local operators

Nozaki

2014

J. High Energ. Phys.

140

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This is an expanded version of the short report arXiv:1401.0539, where we studied the time evolution of (Renyi) entanglement entropies for the excited state defined by acting a given local operator on the ground state. In the present paper, we introduce (Renyi) entanglement entropies of given local operators which are defined by late time values of excesses of (Renyi) entanglement entropies. They measure the degrees of freedom of local operators and characterize them in conformal field theories from the viewpoint of quantum entanglement. We explain how to compute them in free massless scalar field theories and we also investigate their time evolution. Our results can be interpreted in terms of the relativistic propagation of entangled pairs. The main new results which we acquire in the present paper are as follows. Firstly, we provide an explanation which shows that (Renyi) entanglement entropies of a specific operator are given by (Renyi) entanglement entropies whose reduced density matrices are given by the binomial distribution. That operator is constructed of only the scalar field. Secondly, we found the sum rule which (Renyi) entanglement entropies of those local operators obey. Those local operators are located separately. Moreover we argue that (Renyi) entanglement entropies of specific operators in conformal field theories are given by (Renyi) entanglement entropies whose reduced density matrices are given by the binomial distribution. These specific operators are constructed of single-species operators. We also argue that general operators obey the sum rule which we mentioned above.

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Section: Contentsmentioning

confidence: 99%

Notes on quantum entanglement of local operators

Nozaki

2014

J. High Energ. Phys.

140

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“…(47), with the help of Eqs. (A11) and (34), which give ǫ k (Γ) = 4 cos(2θ Γ k ) for Γ = 1. Accordingly, Eq.…”

Section: A Transverse Magnetizationmentioning

confidence: 99%

“…However, their asymptotic stationary state should nonetheless be described by the so-called generalized Gibbs ensemble (GGE) in which each conserved quantity is characterized by a generally different effective temperature [17][18][19][20][21][22][23]. On the other hand, other works [24][25][26][27][28][29][30][31][32][33][34][35] have shown (or at least argued) that this scenario could actually be significantly richer.…”

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confidence: 99%

Dynamic correlations, fluctuation-dissipation relations, and effective temperatures after a quantum quench of the transverse field Ising chain

2012

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Fluctuation-dissipation relations, i.e., the relation between two-time correlation and linear response functions, were successfully used to search for signs of equilibration and to identify effective temperatures in the non-equilibrium behavior of a number of macroscopic classical and quantum systems in contact with thermal baths. Among the most relevant cases in which the effective temperatures thus defined were shown to have a thermodynamic meaning one finds the stationary dynamics of driven super-cooled liquids and vortex glasses, and the relaxation of glasses. Whether and under which conditions an effective thermal behavior can be found in quantum isolated many-body systems after a global quench is a question of current interest. We propose to study the possible emergence of thermal behavior long after the quench by studying fluctuation-dissipation relations in which (possibly time-or frequency-dependent) parameters replace the equilibrium temperature. If thermalization within the Gibbs ensemble eventually occurs these parameters should be constant and equal for all pairs of observables in "partial" or "mutual" equilibrium. We analyze these relations in the paradigmatic quantum system, i.e., the quantum Ising chain, in the stationary regime after a quench of the transverse field. The lack of thermalization to a Gibbs ensemble becomes apparent within this approach. Contents

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“…In this paper we will choose the following profile for M (v) 20) which is always positive and increasing with v. It goes to 0 when v → −∞ and to M when v → +∞. The parameter a > 0 encodes the rapidity of the transition between the two regimes of M (v) ∼ 0 and M (v) ∼ M .…”

Section: Jhep08(2014)051mentioning

confidence: 99%

“…One line of work focuses on constructing holographic duals for quenches in strongly coupled theories [12][13][14][15][16], in the spirit of similar work in weakly coupled quantum field theory involving a sudden change in the parameters of the Hamiltonian [4][5][6][17][18][19][20]. In another approach, the focus has instead been on perturbing the state of the system by turning on homogeneous sources for a short period of time.…”

Section: Introductionmentioning

confidence: 99%

Holographic thermalization with Lifshitz scaling and hyperscaling violation

Fonda

Franti

Keränen

et al. 2014

J. High Energ. Phys.

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A Vaidya type geometry describing gravitation collapse in asymptotically Lifshitz spacetime with hyperscaling violation provides a simple holographic model for thermalization near a quantum critical point with non-trivial dynamic and hyperscaling violation exponents. The allowed parameter regions are constrained by requiring that the matter energy momentum tensor satisfies the null energy condition. We present a combination of analytic and numerical results on the time evolution of holographic entanglement entropy in such backgrounds for different shaped boundary regions and study various scaling regimes, generalizing previous work by Liu and Suh.

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Quantum quench in interacting field theory: A self-consistent approximation

Cited by 132 publications

References 43 publications

Notes on quantum entanglement of local operators

Notes on quantum entanglement of local operators

Dynamic correlations, fluctuation-dissipation relations, and effective temperatures after a quantum quench of the transverse field Ising chain

Holographic thermalization with Lifshitz scaling and hyperscaling violation

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