Information propagation in isolated quantum systems

Luitz, David J.; Lev, Yevgeny Bar

doi:10.1103/physrevb.96.020406

Cited by 172 publications

(168 citation statements)

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“…In this region, the volume occupied by a typical wavefunction scales as anomalous power, D, of the full Hilbert space volume that continuously changes from D = 0 in the insulator to D = 1 in a fully delocalized state. In a qualitative agreement several groups have found that the dynamics in this region is often described by non-trivial power laws that are neither diffusive nor localized [6][7][8][9].…”

Section: Introductionsupporting

confidence: 53%

Multifractal metal in a disordered Josephson junctions array

et al. 2017

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We report the results of the numerical study of the non-dissipative quantum Josephson junction chain with the focus on the statistics of many-body wave functions and local energy spectra. The disorder in this chain is due to the random offset charges. This chain is one of the simplest physical systems to study many-body localization. We show that the system may exhibit three distinct regimes: insulating, characterized by the full localization of many-body wavefunctions, fully delocalized (metallic) one characterized by the wavefunctions that take all the available phase volume and the intermediate regime in which the volume taken by the wavefunction scales as a non-trivial power of the full Hilbert space volume. In the intermediate, non-ergodic regime the Thouless conductance (generalized to many-body problem) does not change as a function of the chain length indicating a failure of the conventional single-parameter scaling theory of localization transition. The local spectra in this regime display the fractal structure in the energy space which is related with the fractal structure of wave functions in the Hilbert space. A simple theory of fractality of local spectra is proposed and a new scaling relationship between fractal dimensions in the Hilbert and energy space is suggested and numerically tested.

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Section: Introductionsupporting

confidence: 53%

Multifractal metal in a disordered Josephson junctions array

et al. 2017

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“…Several experimental proposals have also appeared recently [33][34][35] that enable one to measure OTO correlators and scrambling and three preliminary experiments have already been carried out [36][37][38]. There has been a flurry of recent calculations of out-of-time order correlators in a variety of models [39][40][41][42][43][44][45][46][47][48][49][50][51]. There have also been some recent works exploring other formal aspects of these correlators, including fluctuation-dissipation-like theorems [52][53][54][55].…”

Section: ð1:2þmentioning

confidence: 99%

Onset of many-body chaos in the O(N) model

2017

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The growth of commutators of initially commuting local operators diagnoses the onset of chaos in quantum many-body systems. We compute such commutators of local field operators with N components in the (2 þ 1)-dimensional OðNÞ nonlinear sigma model to leading order in 1=N. The system is taken to be in thermal equilibrium at a temperature T above the zero temperature quantum critical point separating the symmetry broken and unbroken phases. The commutator grows exponentially in time with a rate denoted λ L . At large N the growth of chaos as measured by λ L is slow because the model is weakly interacting, and we find λ L ≈ 3.2T=N. The scaling with temperature is dictated by conformal invariance of the underlying quantum critical point. We also show that operators grow ballistically in space with a "butterfly velocity" given by v B =c ≈ 1 where c is the Lorentz-invariant speed of particle excitations in the system. We briefly comment on the behavior of λ L and v B in the neighboring symmetry broken and unbroken phases.

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“…[44] and experimentally in Ref. 45, however spin transport in such systems was not considered.The delocalized phase of one-dimensional systems with local interactions, shows subdiffusive transport [46][47][48][49][50], accompanied by sublinear growth of the entanglement entropy [51][52][53] and intermediate statistics of eigenvalue spacing [54]. Anomalous transport is commonly explained by rare insulating regions, which effectively suppress transport in one-dimensional systems.…”

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confidence: 99%

Spin transport in a long-range-interacting spin chain

Kloss

Lev

2019

Phys. Rev. A

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Using a numerically exact technique we study spin transport and the evolution of spin-density excitation profiles in a disordered spin-chain with long-range interactions, decaying as a power-law, r −α with distance and α < 2. Our study confirms the prediction of recent theories that the system is delocalized in this parameters regime. Moreover we find that for α > 3/2 the underlying transport is diffusive with a transient super-diffusive tail, similarly to the situation in clean long-range systems. We generalize the Griffiths picture to long-range systems and show that it captures the essential properties of the exact dynamics.Introduction.-Many-body localization (MBL) extends the notion of Anderson localization to interacting systems [1]. For local interactions, its existence is well established theoretically [2, 3] and experimentally in one-dimensional systems [4-6] (see [7] for a recent review), but there is evidence of localization also in twodimensional systems [8][9][10][11][12][13]. For long-range interactions the fate of MBL is less clear. Some studies suggest that the many-body localization is stable for α > 2d [14-17], and some claim that the system is delocalized for all α in the thermodynamic limit [17][18][19]. Finite size systems of size L are claimed to exhibit an effective many-body-like localization transition at a critical disorder which scales with the system size (as a power-law for α < 2d), and diverges in the thermodynamic limit [14,16,17,19,20]. Understanding the dynamics of disordered systems with long-range interactions is of great importance to a number of physical systems, such as nuclear spins [21], dipoledipole interactions of vibrational modes [22][23][24], Frenkel excitons [25], nitrogen vacancy centers in diamond [26][27][28][29][30] and polarons [31]. Long range interactions are also common in atomic and molecular systems, where interactions can be dipolar [32][33][34][35][36][37], van der Waals like [32,38], or even of variable range [39][40][41][42]. Some aspects of the dynamics in such systems were studied numerically in Ref. [43], analytically in Ref. [44] and experimentally in Ref. 45, however spin transport in such systems was not considered.The delocalized phase of one-dimensional systems with local interactions, shows subdiffusive transport [46][47][48][49][50], accompanied by sublinear growth of the entanglement entropy [51][52][53] and intermediate statistics of eigenvalue spacing [54]. Anomalous transport is commonly explained by rare insulating regions, which effectively suppress transport in one-dimensional systems. This mechanism is known as the Griffith's picture [48,55,56] (see Ref.[57] for a recent review and also Ref.[58] were rare regions were introduced externally). In dimensions higher than one the Griffiths picture predicts diffusion, since rare regions can be circumvented [56], however approximate numerical studies [8] as also recent experiments [10,11] suggest that at least for short to inter-arXiv:1911.07857v1 [cond-mat.dis-nn]

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Information propagation in isolated quantum systems

Cited by 172 publications

References 60 publications

Multifractal metal in a disordered Josephson junctions array

Multifractal metal in a disordered Josephson junctions array

Onset of many-body chaos in the O(N) model

Spin transport in a long-range-interacting spin chain

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