Apparent slow dynamics in the ergodic phase of a driven many-body localized system without extensive conserved quantities

Lezama, Talía L. M.; Bera, Soumya; Bardarson, Jens H.

doi:10.1103/physrevb.99.161106

Cited by 44 publications

(28 citation statements)

References 56 publications

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“…For local many-body quantum Hamiltonians, the ground states have been found to display multifractal behavior, even in cases for which eigenstates at the center of the many-body spectrum show random-matrix behavior [34,57,60,[89][90][91]. Also, the question of the existence of a multifractal phase in the vicinity of the many-body localization transition as well as its relation to the slow dynamical phases is under active debate [31,57,61,73,74,[92][93][94][95][96]).…”

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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Section: Introductionmentioning

confidence: 99%

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

2019

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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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“…Indeed, the infinite temperature corresponding to the typical states in the spectral bulk prevail over the finite barrier of soft constraint between previously-disjoint sub-blocks of the Hamiltonian and brings the system to the phase where it was before imposing constraints. However, the relations of slow-dynamics phenomena [65] to hard and soft constraints both in many-body systems [6][7][8][9][10][11][12][13][66][67][68][69] and in closely related single-particle disordered models [44,70] is still under debates and consideration. The question of the dynamics and relaxation of highly non-local operators [71] is also in the focus of the research in the community.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Robustness of delocalization to the inclusion of soft constraints in long-range random models

Nosov

Khaymovich

2019

Phys. Rev. B

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Motivated by the constrained many-body dynamics, the stability of the localization-delocalization properties to the inclusion of the soft constraints is addressed in random matrix models. These constraints are modeled by correlations in long-ranged hopping with Pearson correlation coefficient different from zero or unity. Counterintuitive robustness of delocalized phases, both ergodic and (multi)fractal, in these models is numerically observed and confirmed by the analytical calculations. First, matrix inversion trick is used to uncover the origin of such robustness. Next, to characterize delocalized phases a method of eigenstate calculation, sensitive to correlations in long-ranged hopping terms, is developed for random matrix models and approved by numerical calculations and previous analytical ansatz. The effect of the robustness of states in the bulk of the spectrum the inclusion of to soft constraints is generally discussed for single-particle and many-body systems.

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Apparent slow dynamics in the ergodic phase of a driven many-body localized system without extensive conserved quantities

Cited by 44 publications

References 56 publications

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

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

Spin transport in a long-range-interacting spin chain

Robustness of delocalization to the inclusion of soft constraints in long-range random models

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