Dynamics in the Ising field theory after a quantum quench

Schuricht, Dirk; Eßler, Fabian H. L.

doi:10.1088/1742-5468/2012/04/p04017

Cited by 121 publications

(202 citation statements)

References 92 publications

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“…[21,23,30,36,68], the expectation value σ x (t) ofσ x decays to zero at long times for any Γ = Γ 0 . This is comparable to the equilibrium thermal behavior at finite temperature T > 0, which is characterized by the absence of long-range order of the magnetization along the x component.…”

Section: Computation Of the Correlation Functionsmentioning

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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Section: Computation Of the Correlation Functionsmentioning

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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“…The calculation of the time dependence of the order parameter was performed in [26,30]. For quenches, starting in the disordered phase 0 > c H H , the order parameter is zero because the symmetry 2 Z (between states | ±〉 ) remains unbroken [26,31]. According to [26,31] after the quantum quench, which starts in the ordered phase and finishes in the ordered phase 0 1 , < c H H H , the ground-state time dependence of the order parameter is…”

Section: Dynamical Quantum Phase Transitionsmentioning

confidence: 99%

Dynamical quantum phase transitions (Review Article)

Zvyagin

2016

Low Temperature Physics

142

127

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During recent years the interest to dynamics of quantum systems has grown considerably. Quantum many body systems out of equilibrium often manifest behavior, different from the one predicted by standard statistical mechanics and thermodynamics in equilibrium. Since the dynamics of a many-body quantum system typically involve many excited eigenstates, with a non-thermal distribution, the time evolution of such a system provides an unique way for investigation of non-equilibrium quantum statistical mechanics. Last decade such new subjects like quantum quenches, thermalization, pre-thermalization, equilibration, generalized Gibbs ensemble, etc. are among the most attractive topics of investigation in modern quantum physics. One of the most interesting themes in the study of dynamics of quantum many-body systems out of equilibrium is connected with the recently proposed important concept of dynamical quantum phase transitions. During the last few years a great progress has been achieved in studying of those singularities in the time dependence of characteristics of quantum mechanical systems, in particular, in understanding how the quantum critical points of equilibrium thermodynamics affect their dynamical properties. Dynamical quantum phase transitions reveal universality, scaling, connection to the topology, and many other interesting features. Here we review the recent achievements of this quickly developing part of low-temperature quantum physics. The study of dynamical quantum phase transitions is especially important in context of their connection to the problem of the modern theory of quantum information, where namely non-equilibrium dynamics of many-body quantum system plays the major role. PACS

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“…In order to draw a comparison between relaxation to the stationary state in the thermodynamic limit and finite-size corrections in finite chains we focus on quenches in the transverse field Ising chain, where recently the time dependence of correlation functions has been computed exactly 24,28,51,53,54 . We note that our discussion generalizes straightforwardly to other spin chains with free fermion spectra, like the quantum XY model.…”

Section: The Modelmentioning

confidence: 99%

Finite-size corrections versus relaxation after a sudden quench

Fagotti

2013

Phys. Rev. B

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We consider the time evolution after sudden quenches of global parameters in translational invariant Hamiltonians and study the time average expectation values and entanglement entropies in finite chains. We show that in noninteracting models the time average of spin correlation functions is asymptotically equal to the infinite time limit in the infinite chain, which is known to be described by a generalized Gibbs ensemble. The equivalence breaks down considering nonlocal operators, and we establish that this can be traced back to the existence of conservation laws common to the Hamiltonian before and after the quench. We develop a method to compute the leading finite-size correction for time average correlation functions and entanglement entropies. We find that large corrections are generally associated to observables with slow relaxation dynamics.

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Dynamics in the Ising field theory after a quantum quench

Cited by 121 publications

References 92 publications

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

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

Dynamical quantum phase transitions (Review Article)

Finite-size corrections versus relaxation after a sudden quench

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