Quench dynamics across quantum critical points

Sengupta, K.; Powell, Stephen; Sachdev, Subir

doi:10.1103/physreva.69.053616

Cited by 291 publications

(373 citation statements)

References 11 publications

(26 reference statements)

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“…We discuss the effective "generic" thermalization induced by integrability breaking, by analyzing the changes in the space asymptotics of the order parameter correlators, after a quench in the transverse-field strength Γ: as discussed in Sec. IV B, for quenches crossing the Ising quantum critical point from the paramagnetic to the ferromagnetic side, non-thermal sinusoidal oscillations in real space naturally emerge 15,52 . Below we numerically show that a non-integrable perturbation leads to a suppression of them, thus driving the system towards a completely thermal-like behavior, where only the exponential decay in space of correlations is present.…”

Section: Sensitivity To the Breaking Of Integrabilitymentioning

confidence: 99%

Long time dynamics following a quench in an integrable quantum spin chain: Local versus nonlocal operators and effective thermal behavior

et al. 2010

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We study the dynamics of the quantum Ising chain following a zero-temperature quench of the transverse field strength. Focusing on the behavior of two-point spin correlation functions, we show that the correlators of the order parameter display an effective asymptotic thermal behavior, i.e., they decay exponentially to zero, with a phase coherence rate and a correlation length dictated by the equilibrium law with an effective temperature set by the energy of the initial state. On the contrary, the two-point correlation functions of the transverse magnetization or the density-of-kinks operator decay as a power-law and do not exhibit thermal behavior. We argue that the different behavior is linked to the locality of the corresponding operator with respect to the quasi-particles of the model: non-local operators, such as the order parameter, behave thermally, while local ones do not. We study which features of the two-point correlators are a consequence of the integrability of the model by analizing their robustness with respect to a sufficiently strong integrability-breaking term.

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Section: Sensitivity To the Breaking Of Integrabilitymentioning

confidence: 99%

Long time dynamics following a quench in an integrable quantum spin chain: Local versus nonlocal operators and effective thermal behavior

et al. 2010

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“…7) with H a block circulant matrix (apart from boundary terms), that is to say 1.7)). The dimension d of the blocks depends on the spin interaction.…”

Section: Quenches In Noninteracting Spin Chainsmentioning

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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“…Recently, Sengupta et al [14] have studied time evolution of the Ising order correlations under a time-dependent transverse field and shown that the order parameter is best enhanced in the vicinity of the quantum critical point. Quan et al [15] have studied transition dynamics of a quantum two-level system from a pure state to a mixed one induced by the quantum criticality of the surrounding many-body system.…”

mentioning

confidence: 99%

Loschmidt echo and Berry phase of a quantum system coupled to anXYspin chain: Proximity to a quantum phase transition

Yuan

Zhang

2007

Phys. Rev. A

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We study the Loschmidt echo (LE) of a coupled system consisting of a central spin and its surrounding environment described by a general XY spin-chain model. The quantum dynamics of the LE is shown to be remarkably influenced by the quantum criticality of the spin chain. In particular, the decaying behavior of the LE is found to be controlled by the anisotropy parameter of the spin chain. Furthermore, we show that due to the coupling to the spin chain, the groundstate Berry phase for the central spin becomes nonanalytical and its derivative with respect to the magnetic parameter λ in spin chain diverges along the critical line λ = 1, which suggests an alternative measurement of the quantum criticality of the spin chain.

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Quench dynamics across quantum critical points

Cited by 291 publications

References 11 publications

Long time dynamics following a quench in an integrable quantum spin chain: Local versus nonlocal operators and effective thermal behavior

Long time dynamics following a quench in an integrable quantum spin chain: Local versus nonlocal operators and effective thermal behavior

Finite-size corrections versus relaxation after a sudden quench

Loschmidt echo and Berry phase of a quantum system coupled to anXYspin chain: Proximity to a quantum phase transition

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