Low-frequency behavior of off-diagonal matrix elements in the integrable XXZ chain and in a locally perturbed quantum-chaotic XXZ chain

Brenes, Marlon; Goold, John; Rigol, Marcos

doi:10.1103/physrevb.102.075127

Cited by 59 publications

(56 citation statements)

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“…The single-defect X X Z model has motivated studies of transport behavior in single-defect noninteracting models [38] and searches for minimal chaotic models with electronphonon coupling [39], but it was not until the beginning of 2020 that the model saw a significant resurgence of interest. It has since been employed in studies of many-body quantum chaos [40,41], thermalization [42,43], quantum transport [44,45], and entanglement [46]. In the present work, we show that the onset of chaos due to a local onsite perturbation is not unique to the X X Z model.…”

Section: Introductionmentioning

confidence: 48%

“…This is referred to as the diagonal ETH and has been verified for the single-defect X X Z model in [35,36] and recently in [42]. In chaotic systems, the distribution of the off-diagonal matrix elements of local operators is Gaussian [52,53], which is called the off-diagonal ETH and has been confirmed for the single-defect X X Z model as well [44].…”

Section: Eigenstate Thermalization Hypothesismentioning

confidence: 73%

“…In Ref. [52] (see also [44,[53][54][55]), the distinction between integrable and chaotic models is based on the distribution of the off-diagonal matrix elements of local observables in each subspace. In Refs.…”

Section: Introductionmentioning

confidence: 99%

“…The ratio R from Eq. (5) vs ω for the Ising model (c) and spin-1 model (d) in the chaotic regime, d = 0.8.Following[44], we consider only the eigenstates for which…”

mentioning

confidence: 99%

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Speck of chaos

Santos

Pérez‐Bernal

Torres-Herrera

2020

Phys. Rev. Research

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It has been shown that, despite being local, a perturbation applied to a single site of the one-dimensional X X Z model is enough to bring this interacting integrable spin-1/2 system to the chaotic regime. Here, we show that this is not unique to this model, but happens also to the Ising model in a transverse field and to the spin-1 Lai-Sutherland chain. The larger the system is, the smaller the amplitude of the local perturbation for the onset of chaos. We focus on two indicators of chaos, the correlation hole, which is a dynamical tool, and the distribution of off-diagonal elements of local observables, which is used in the eigenstate thermalization hypothesis. Both methods avoid spectrum unfolding and can detect chaos even when the eigenvalues are not separated by symmetry sectors.

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Section: Introductionmentioning

confidence: 48%

Section: Eigenstate Thermalization Hypothesismentioning

confidence: 73%

Section: Introductionmentioning

confidence: 99%

“…The ratio R from Eq. (5) vs ω for the Ising model (c) and spin-1 model (d) in the chaotic regime, d = 0.8.Following[44], we consider only the eigenstates for which…”

mentioning

confidence: 99%

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Speck of chaos

Santos

Pérez‐Bernal

Torres-Herrera

2020

Phys. Rev. Research

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show abstract

“…Interestingly, it was recently observed that the function |f (�)| 2 can be defined and remains smooth even in generic integrable systems 72 . Then |f (�)| 2 vanishes as → 0 for deformations of the Hamiltonian along integrable directions 44,[73][74][75] .…”

Section: Persistent Dark States Away From the Integrable Lines Inmentioning

confidence: 99%

Persistent dark states in anisotropic central spin models

Villazon

Claeys

Pandey

et al. 2020

Sci Rep

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Long-lived dark states, in which an experimentally accessible qubit is not in thermal equilibrium with a surrounding spin bath, are pervasive in solid-state systems. We explain the ubiquity of dark states in a large class of inhomogeneous central spin models using the proximity to integrable lines with exact dark eigenstates. At numerically accessible sizes, dark states persist as eigenstates at large deviations from integrability, and the qubit retains memory of its initial polarization at long times. Although the eigenstates of the system are chaotic, exhibiting exponential sensitivity to small perturbations, they do not satisfy the eigenstate thermalization hypothesis. Rather, we predict long relaxation times that increase exponentially with system size. We propose that this intermediate chaotic but non-ergodic regime characterizes mesoscopic quantum dot and diamond defect systems, as we see no numerical tendency towards conventional thermalization with a finite relaxation time.

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Krylov localization and suppression of complexity

Rabinovici

Sánchez-Garrido

Shir

et al. 2022

J. High Energ. Phys.

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Quantum complexity, suitably defined, has been suggested as an important probe of late-time dynamics of black holes, particularly in the context of AdS/CFT. A notion of quantum complexity can be effectively captured by quantifying the spread of an operator in Krylov space as a consequence of time evolution. Complexity is expected to behave differently in chaotic many-body systems, as compared to integrable ones. In this paper we investigate Krylov complexity for the case of interacting integrable models at finite size and find that complexity saturation is suppressed as compared to chaotic systems. We associate this behavior with a novel localization phenomenon on the Krylov chain by mapping the theory of complexity growth and spread to an Anderson localization hopping model with off-diagonal disorder, and find that localization is enhanced in the integrable case due to a stronger disorder in the hopping amplitudes, inducing an effective suppression of Krylov complexity. We demonstrate this behavior for an interacting integrable model, the XXZ spin chain, and show that the same behavior results from a phenomenological model that we define: this model captures the essential features of our analysis and is able to reproduce the behaviors we observe for chaotic and integrable systems via an adjustable disorder parameter.

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Low-frequency behavior of off-diagonal matrix elements in the integrable XXZ chain and in a locally perturbed quantum-chaotic XXZ chain

Cited by 59 publications

References 50 publications

Speck of chaos

Speck of chaos

Persistent dark states in anisotropic central spin models

Krylov localization and suppression of complexity

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