Ergodicity breaking in an incommensurate system observed by OTOCs and loschmidt echoes: From quantum diffusion to sub-diffusion

Lozano-Negro, Fabricio S.; Zangara, Pablo R.; Pastawski, Horacio M.

doi:10.1016/j.chaos.2021.111175

Cited by 13 publications

(2 citation statements)

References 63 publications

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“…Based on a phenomenological model called the weak link model [48], it was shown that starting from a model with short-ranged interaction, increasing the disorder strength impedes the information propagation and drives a series of transitions of the lightcone function from linear t ∼ r to algebraic t ∼ r ξ (ξ > 1) and eventually becomes exponential log t ∼ r when the system becomes many-body localized. Similar transitions are found in quasi-periodic systems as well [52,53].…”

Section: B Scrambling Dynamics In Geometrically Local Systemssupporting

confidence: 79%

Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial

Xu¹,

Swingle²

2022

Preprint

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This tutorial article introduces the physics of quantum information scrambling in quantum manybody systems. The goals are to understand how to quantify the spreading of quantum information precisely and how causality emerges in complex quantum systems. We introduce the general framework to study the dynamics of quantum information, including detection and decoding. We show that the dynamics of quantum information is closely related to operator dynamics in the Heisenberg picture, and, in certain circumstances, can be precisely quantified by the so-called out-the-time ordered correlator (OTOC). The general behavior of OTOC is discussed based on several toy models, including the Sachdev-Ye-Kitaev model, random circuit models, and Brownian models, in which OTOC is analytically tractable. We introduce numerical methods, both exact diagonalization and tensor network methods, to calculate OTOC for generic quantum many-body systems. We also survey current experiment schemes to measure OTOC in various quantum simulators.

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Section: B Scrambling Dynamics In Geometrically Local Systemssupporting

confidence: 79%

Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial

Xu¹,

Swingle²

2022

Preprint

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“…Then, a time reversed evolution is imposed for a new period t, producing the evolved density matrix exp[−iHt]V W (t)V † exp[iHt] used to evaluate an observable, say W † . In an NMR MQC experiment V is a global rotation, such a Zeeman pulse V = exp[−iI z θ] [56] or a field gradient pulse [83]. Such perturbation labels with a phase θ n the participation of superposition state whose total spin projection differs in n. Technically, one measures the total in-plane polarization D= I x .…”

Section: Connections With Otocs and Quantum Chaosmentioning

confidence: 99%

Emergent decoherence induced by quantum chaos in a many-body system: A Loschmidt echo observation through NMR

Sánchez,

Chattah,

Pastawski

2021

Preprint

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In the long quest to identify and compensate the sources of decoherence in many-body systems far from the ground state, the varied family of Loschmidt echoes (LEs) became an invaluable tool in several experimental techniques. A LE involves a time-reversal procedure to assess the effect of perturbations in a quantum excitation dynamics. However, when addressing macroscopic systems one is repeatedly confronted with limitations that seem insurmountable. This led to formulate the central hypothesis of irreversibility stating that the time-scale of decoherence, T3, is proportional to the time-scale of the many-body interactions we reversed, T2. We test this by implementing two experimental schemes based on Floquet Hamiltonians where the effective strength of the dipolar spinspin coupling, i.e. 1/T2, is reduced by a variable scale factor k. This extends the perturbations time scale, TΣ, in relation to T2. Strikingly, we observe the superposition of the normalized Loschmidt echoes for the bigger values of k. This manifests the dominance of the intrinsic dynamics over the perturbation factors, even when the Loschmidt echo is devised to reverse that intrinsic dynamics. Thus, in the limit where the reversible interactions dominate over perturbations, the LE decays within a time-scale, T3 ≈ T2/R with R = (0.15 ± 0.01), confirming the emergence of a perturbation independent regime. These results support the central hypothesis of irreversibility.

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Low perturbation limit decoherence analyzed by scaling the Double Quantum Hamiltonian

Sánchez¹,

Pastawski²,

Chattah³

2023

Journal of Magnetic Resonance Open

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Ergodicity breaking in an incommensurate system observed by OTOCs and loschmidt echoes: From quantum diffusion to sub-diffusion

Cited by 13 publications

References 63 publications

Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial

Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial

Emergent decoherence induced by quantum chaos in a many-body system: A Loschmidt echo observation through NMR

Low perturbation limit decoherence analyzed by scaling the Double Quantum Hamiltonian

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