Sensitivity to small perturbations in systems of large quantum spins

Elsayed, Tarek A.; Fine, Boris V.

doi:10.1088/0031-8949/2015/t165/014011

Cited by 33 publications

(38 citation statements)

References 31 publications

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“…(8) to the basis of LI-OMS using Eqs. (9) and (10). Under the assumption that σ z 1 commutes with the Hamiltonian [this is equivalent to retaining only first term in the expansion of σ z 1 over LIOMS, Eq.…”

Section: Decay Of Spin Coherence With Timementioning

confidence: 99%

“…In the non-interacting case the coefficients c i in the expansion (10) are given by the tails of the single-particle wave function. Using log-normal form of the distribution of the inverse localization length, 51 we replace ϕ ci (t) with an asymptotic form of the characteristic function of the log-normal distribution …”

Section: 50mentioning

confidence: 99%

“…10 Finally, connections between Loschmidt echo revivals and quantum criticality were also recently discussed.…”

Section: Introductionmentioning

confidence: 99%

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Loschmidt echo in many-body localized phases

Serbyn¹,

Abanin²

2017

Phys. Rev. B

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The Loschmidt echo, defined as the overlap between quantum wave function evolved with different Hamiltonians, quantifies the sensitivity of quantum dynamics to perturbations and is often used as a probe of quantum chaos. In this work we consider the behavior of the Loschmidt echo in the many body localized phase, which is characterized by emergent local integrals of motion, and provides a generic example of non-ergodic dynamics. We demonstrate that the fluctuations of the Loschmidt echo decay as a power law in time in the many-body localized phase, in contrast to the exponential decay in few-body ergodic systems. We consider the spin-echo generalization of the Loschmidt echo, and argue that the corresponding correlation function saturates to a finite value in localized systems. Slow, power-law decay of fluctuations of such spin-echo-type overlap is related to the operator spreading and is present only in the many-body localized phase, but not in a non-interacting Anderson insulator. While most of the previously considered probes of dephasing dynamics could be understood by approximating physical spin operators with local integrals of motion, the Loschmidt echo and its generalizations crucially depend on the full expansion of the physical operators via local integrals of motion operators, as well as operators which flip local integrals of motion. Hence, these probes allow to get insights into the relation between physical operators and local integrals of motion, and access the operator spreading in the many-body localized phase.

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Section: Decay Of Spin Coherence With Timementioning

confidence: 99%

Section: 50mentioning

confidence: 99%

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Loschmidt echo in many-body localized phases

Serbyn¹,

Abanin²

2017

Phys. Rev. B

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“…Quantum-mechanical description of Loschmidt echoes involves OTOCs [16,17,22,23,28,[47][48][49][50][51][52][53][54][55][56]. We now illustrate that the parameter Λ defined in the present work from the relation…”

Section: Relation To Quantum Systemsmentioning

confidence: 90%

“…Various aspects of this work are relevant to the previous investigations of lattice gauge models [9][10][11][12][13] and spin lattice models [14][15][16][17]. We also note that our method involves the classical counterpart of out-of-timeorder quantum correlators (OTOCs) [18] that have been actively investigated in recent years in the context of quantum thermalization [19][20][21][22][23] and many-body localization problems [24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Estimating ergodization time of a chaotic many-particle system from a time reversal of equilibrium noise

Tarkhov

Fine

2018

New J. Phys.

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We propose a method of estimating ergodization time of a chaotic many-particle system by monitoring equilibrium noise before and after time reversal of dynamics(Loschmidt echo). The ergodization time is defined as the characteristic time required to extract the largest Lyapunov exponent from a system's dynamics. We validate the method by numerical simulation of an array of coupled Bose-Einstein condensates in the regime describable by the discrete Gross-Pitaevskii equation. The quantity of interest for the method is a counterpart of out-of-time-order correlators in the quantum regime. Outline of the methodIn figure 1, we outline the method. It consists of the following steps.

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Unifying scrambling, thermalization and entanglement through measurement of fidelity out-of-time-order correlators in the Dicke model

Lewis-Swan

Safavi-Naini

Bollinger³

et al. 2019

Nat Commun

222

197

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Scrambling is the process by which information stored in local degrees of freedom spreads over the many-body degrees of freedom of a quantum system, becoming inaccessible to local probes and apparently lost. Scrambling and entanglement can reconcile seemingly unrelated behaviors including thermalization of isolated quantum systems and information loss in black holes. Here, we demonstrate that fidelity out-of-time-order correlators (FOTOCs) can elucidate connections between scrambling, entanglement, ergodicity and quantum chaos (butterfly effect). We compute FOTOCs for the paradigmatic Dicke model, and show they can measure subsystem Rényi entropies and inform about quantum thermalization. Moreover, we illustrate why FOTOCs give access to a simple relation between quantum and classical Lyapunov exponents in a chaotic system without finite-size effects. Our results open a path to experimental use FOTOCs to explore scrambling, bounds on quantum information processing and investigation of black hole analogs in controllable quantum systems.

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Sensitivity to small perturbations in systems of large quantum spins

Cited by 33 publications

References 31 publications

Loschmidt echo in many-body localized phases

Loschmidt echo in many-body localized phases

Estimating ergodization time of a chaotic many-particle system from a time reversal of equilibrium noise

Unifying scrambling, thermalization and entanglement through measurement of fidelity out-of-time-order correlators in the Dicke model

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