Multifractal metal in a disordered Josephson junctions array

Pino, Manuel del; Kravtsov, V. E.; Altshuler, B. L.; Ioffe, L. B.

doi:10.1103/physrevb.96.214205

Cited by 57 publications

(53 citation statements)

References 48 publications

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“…Energy spectrum of the kinetic part of the Hamiltonian is limited to the stripe E ∈ (−N Γ, +N Γ). For the energies E = N outside of this band (that is, | | > Γ) the Green function can be found from (14) by the Laplace transform and further saddle-point integration (using N 1 condition):…”

Section: Matrix Elements: Analytic Derivation and Numerical Resultsmentioning

confidence: 99%

Non-ergodic extended phase of the Quantum Random Energy model

2019

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The concept of non-ergodicity in quantum many body systems can be discussed in the context of the wave functions of the many body system or as a property of the dynamical observables, such as time-dependent spin correlators. In the former approach the non-ergodic delocalized states is defined as the one in which the wave functions occupy a volume that scales as a non-trivial power of the full phase space. In this work we study the simplest spin glass model and find that in the delocalized non-ergodic regime the spin-spin correlators decay with the characteristic time that scales as non-trivial power of the full Hilbert space volume. The long time limit of this correlator also scales as a power of the full Hilbert space volume. We identify this phase with the glass phase whilst the many body localized phase corresponds to a 'hyperglass' in which dynamics is practically absent. We discuss the implications of these finding to quantum information problems. arXiv:1812.06016v2 [cond-mat.dis-nn]

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Section: Matrix Elements: Analytic Derivation and Numerical Resultsmentioning

confidence: 99%

Non-ergodic extended phase of the Quantum Random Energy model

2019

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“…The most interesting property of the RP model is the existence of a finite region of non-ergodic extended states. Such a region appears at the metallic side of the many-body localization transition in an array of Josephson junctions [23,24,25,26,27]. This nonergodic behaviour has also been analyzed in other quantum systems [28,29,30,31,32] and it has been suggested that it can play an important role for quantum information [33].…”

Section: Introductionmentioning

confidence: 99%

From ergodic to non-ergodic chaos in Rosenzweig–Porter model

Pino

Tabanera

Serna

2019

J. Phys. A: Math. Theor.

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The Rosenzweig-Porter model is a one-parameter family of random matrices with three different phases: ergodic, extended non-ergodic and localized. We characterize numerically each of these phases and the transitions between them. We focus on several quantities that exhibit non-analytical behaviour and show that they obey the scaling hypothesis. Based on this, we argue that non-ergodic chaotic and ergodic regimes are separated by a continuous phase transition, similarly to the transition between non-ergodic chaotic and localized phases.

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“…Multifractal statistics appears at the Anderson localization transition for single-particle lattice systems [17,[65][66][67][68][69][70][71]. In addition, recent examples have reported (multi)fractal phases extend-ing over a whole range of parameters [72][73][74][75][76][77][78][79][80][81][82][83][84][85][86]. Multifractal wavefunctions have been found for some quantum maps [68,70,87,88].…”

Section: Introductionmentioning

confidence: 99%

Multifractal dimensions for random matrices, chaotic quantum maps, and many-body systems

2019

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Multifractal dimensions allow for characterizing the localization properties of states in complex quantum systems. For ergodic states the finite-size versions of fractal dimensions converge to unity in the limit of large system size. However, the approach to the limiting behavior is remarkably slow. Thus, an understanding of the scaling and finite-size properties of fractal dimensions is essential. We present such a study for random matrix ensembles, and compare with two chaotic quantum systems -the kicked rotor and a spin chain. For random matrix ensembles we analytically obtain the finite-size dependence of the mean behavior of the multifractal dimensions, which provides a lower bound to the typical (logarithmic) averages. We show that finite statistics has remarkably strong effects, so that even random matrix computations deviate from analytic results (and show strong sample-to-sample variation), such that restoring agreement requires exponentially large sample sizes. For the quantized standard map (kicked rotor) the multifractal dimensions are found to follow the random matrix predictions closely, with the same finite statistics effects. For a XXZ spin-chain we find significant deviations from the random matrix prediction -the large-size scaling follows a system-specific path towards unity. This suggests that local many-body Hamiltonians are "weakly ergodic", in the sense that their eigenfunction statistics deviate from random matrix theory. arXiv:1905.03099v2 [cond-mat.stat-mech]

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Multifractal metal in a disordered Josephson junctions array

Cited by 57 publications

References 48 publications

Non-ergodic extended phase of the Quantum Random Energy model

Non-ergodic extended phase of the Quantum Random Energy model

From ergodic to non-ergodic chaos in Rosenzweig–Porter model

Multifractal dimensions for random matrices, chaotic quantum maps, and many-body systems

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