Anomalous Diffusion and Localization in a Positionally Disordered Quantum Spin Array

Menu, Raphaël; Roscilde, Tommaso

doi:10.1103/physrevlett.124.130604

Cited by 17 publications

(7 citation statements)

References 45 publications

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“…for kicked or multi-species models), the growth is fast, with a rate related to Lyapunov exponents. Interestingly, also longbut-finite-range interactions open up a finite layer of instability with fast entanglement growth, due to the presence of a chaotic dynamical phase (Lerose et al, 2018(Lerose et al, , 2019c Correlation spreading with van der Walls interactions and the presence of positional disorder in 2D was investigated in (Menu and Roscilde, 2020). Multifractality and localization of spin-wave excitations above a ferromagnetic ground state are observed.…”

Section: B Lieb-robinson Boundmentioning

confidence: 99%

Long-range interacting quantum systems

Defenu,

Donner,

Macrì

et al. 2021

Preprint

108

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The presence of non-local and long-range interactions in quantum systems induces several peculiar features in their equilibrium and out-of-equilibrium behavior. In current experimental platforms control parameters such as interaction range, temperature, density and dimension can be changed. The existence of universal scaling regimes, where diverse physical systems and observables display quantitative agreement, generates a common framework, where the efforts of different research communities can be -in some cases rigorously -connected. Still, the application of this general framework to particular experimental realisations requires the identification of the regimes where the universality phenomenon is expected to appear. In the present review we summarise the recent investigations of many-body quantum systems with long-range interactions, which are currently realised in Rydberg atom arrays, dipolar systems, trapped ion setups and cold atoms in cavity experiments. Our main aim is to present and identify the common and (mostly) universal features induced by long-range interactions in the behaviour of quantum many-body systems. We will discuss both the case of very strong non-local couplings, i.e. the non-additive regime, and the one in which energy is extensive, but nevertheless low-energy, long wavelength properties are altered with respect to the short-range limit. Cases of competition with other local effects in the above mentioned setups are also reviewed.

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Section: B Lieb-robinson Boundmentioning

confidence: 99%

Long-range interacting quantum systems

Defenu,

Donner,

Macrì

et al. 2021

Preprint

108

View full text Add to dashboard Cite

show abstract

“…B) to the q = 0 one. A similar approach has been used in a variety of recent studies, and it is successful for systems that do not possess the zero-mode pathology descending from U(1) symmetry [39][40][41][42][43]. For systems with U(1) symmetry, gapping out the zero mode as in LSW+h theory is not an option away from equilibrium, because the application of a field is only justified when requesting the average collective spin to vanish.The latter average is instead maximal at t = 0 in the particular quench scheme that we are considering.…”

Section: B Non-equilibrium Lsw Theory and Squeezing Dynamicsmentioning

confidence: 99%

Spin squeezing from bilinear spin-spin interactions: Two simple theorems

2021

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The non-equilibrium dynamics of quantum spin models is a most challenging topic, due to the exponentiality of Hilbert space; and it is central to the understanding of the many-body entangled states that can be generated by state-of-the-art quantum simulators. A particularly important class of evolutions is the one governed by U(1) symmetric Hamiltonians, initialized in a state which breaks the U(1) symmetry -the paradigmatic example being the evolution of the so-called one-axistwisting (OAT) model, featuring infinite-range interactions between spins. In this work we show that the dynamics of the OAT model can be closely reproduced by systems with power-law-decaying interactions, thanks to an effective separation between the zero-momentum degrees of freedom, associated with the so-called Anderson tower of states, and reconstructing a OAT model; and finitemomentum ones, associated with spin-wave excitations. This mechanism explains quantitatively the recent numerical observation of spin squeezing and Schrödinger-cat generation in the dynamics of dipolar Hamiltonians; and it paves the way for the extension of this observation to a much larger class of models of immediate relevance for quantum simulations.

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“…Our results indicate that the various diffusion coefficients are thoroughly interconnected with the specific geometries of fluctuations constituting the measured series. The connection between multifractality and various models of anomalous diffusion is also being noticed both theoretically [51,[179][180][181][182] and empirically [162,163,168,[183][184][185][186]. Multifractal formalisms and anomalous-diffusion processes thus appear to be entwined in a vibrant, expanding, far-reaching, and synergistic relationship originating from the out-ofequilibrium character, lack of detailed balance, and of time-reversal symmetry, multiscale nature, nonlinearity and multi-body interactions that typify living and evolv-FIG.…”

Section: Discussionmentioning

confidence: 99%

Ergodic characterization of non-ergodic anomalous diffusion processes

Mangalam¹,

Metzler²,

Kelty-Stephen³

2023

Preprint

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Anomalous diffusion in a variety of complex systems abounds in nature and spans multiple space and time scales. Canonical characterization techniques that rely upon mean squared displacement (MSD) break down for non-ergodic processes, making it challenging to characterize anomalous diffusion from an individual time-series measurement. Non-ergodicity reigns when the time-averaged mean square displacement TA-MSD differs from the ensemble-averaged mean squared displacement EA-MSD even in the limit of long measurement series. In these cases, the typical theoretical results for ensemble averages cannot be used to understand and interpret data acquired from time averages. The difficulty then lies in obtaining statistical descriptors of the measured diffusion process that are not non-ergodic. We show that linear descriptors such as the standard deviation (SD), coefficient of variation (CV ), and root mean square (RM S) break ergodicity in proportion to nonergodicity in the diffusion process. In contrast, time series of descriptors addressing sequential structure and its potential nonlinearity: multifractality change in a time-independent way and fulfill the ergodic assumption, largely independent of the time series' non-ergodicity. We show that these findings follow the multiplicative cascades underlying these diffusion processes. Adding fractal and multifractal descriptors to typical linear descriptors would improve the characterization of anomalous diffusion processes. Two particular points bear emphasis here. First, as an appropriate formalism for encoding the nonlinearity that might generate non-ergodicity, multifractal modeling offers descriptors that can behave ergodically enough to meet the needs of linear modeling. Second, this capacity to describe non-ergodic processes in ergodic terms offers the possibility that multifractal modeling could unify several disparate non-ergodic diffusion processes into a common framework.

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Anomalous Diffusion and Localization in a Positionally Disordered Quantum Spin Array

Cited by 17 publications

References 45 publications

Long-range interacting quantum systems

Long-range interacting quantum systems

Spin squeezing from bilinear spin-spin interactions: Two simple theorems

Ergodic characterization of non-ergodic anomalous diffusion processes

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