Transport in quasiperiodic interacting systems: From superdiffusion to subdiffusion

Lev, Yevgeny Bar; Kennes, Dante M.; Klöckner, C.; Reichman, David R.; Karrasch, Christoph

doi:10.1209/0295-5075/119/37003

Cited by 74 publications

(31 citation statements)

References 61 publications

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“…Importantly, comparing both cases we cannot detect an essential difference in the evolution of ∆x(t) with the inhomogeneity strength. Therefore, our results seem hard to reconcile with Griffiths-type scenarios that rely on rare-regions to explain the origin of slow dynamics 26,28,29,46 .…”

Section: Introductioncontrasting

confidence: 64%

Slow dynamics and strong finite-size effects in many-body localization with random and quasiperiodic potentials

2019

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We investigate charge relaxation in disordered and quasi-periodic quantum-wires of spin-less fermions (t−V -model) at different inhomogeneity strength W in the localized and nearly-localized regime. Our observable is the time-dependent density correlation function, Φ(x, t), at infinite temperature. We find that disordered and quasi-periodic models behave qualitatively similar: Although even at longest observation times the width ∆x(t) of Φ(x, t) does not exceed significantly the noninteracting localization length, ξ0, strong finite-size effects are encountered. Our findings appear difficult to reconcile with the rare-region physics (Griffiths effects) that often is invoked as an explanation for the slow dynamics observed by us and earlier computational studies. Motivated by our numerical data we discuss a scenario in which the MBL-phase splits into two subphases: in MBLA ∆x(t) diverges slower than any power, while it converges towards a finite value in MBLB . Within the scenario the transition between MBLA and the ergodic phase is characterized by a length scale, ξ, that exhibits an essential singularity ln ξ ∼ 1/|W − Wc 1 |. Relations to earlier numerics and proposals of two-phase scenarios will be discussed. arXiv:1904.06928v2 [cond-mat.str-el]

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Section: Introductioncontrasting

confidence: 64%

Slow dynamics and strong finite-size effects in many-body localization with random and quasiperiodic potentials

2019

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“…While our study is inline with the generalized Griffiths picture it is possible that absence of anomalous transport in disordered longrange chains is related to the absence of localization. This concern is pertinent given previously observed inconsistencies of the Griffiths picture [8,81] (cf. [82,83], and see also the very recent [84]), suggesting that our understanding of the mechanism of anomalous transport in the vicinity of the MBL transition is far from being complete.…”

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confidence: 90%

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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“…The reason for these behaviors is the existence of localized quasi-particles (often called l-bits) in the many-body localized phase [12][13][14][15][16][17] that form an extensive set of conserved quantities (see [10,18,19] for a review). Curiously, the conductivity does not behave according to the naive expectation (i.e., vanishing conductivities in the MBL phase and finite ones in the ergodic phase): in the MBL phase, numerical studies report vanishingly small dc conductivities, consistent with a perfect insulator, while in the ergodic phase, some studies report finite dc-conductivities [20,21], while others provide evidence for subdiffusive dynamics [4,[22][23][24][25] (see also [26] for a critical discussion and [27] for a review).…”

Section: Introductionmentioning

confidence: 97%

Many-body localization of spinless fermions with attractive interactions in one dimension

et al. 2018

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We study the finite-energy density phase diagram of spinless fermions with attractive interactions in one dimension in the presence of uncorrelated diagonal disorder. Unlike the case of repulsive interactions, a delocalized Luttinger-liquid phase persists at weak disorder in the ground state, which is a well-known result. We revisit the ground-state phase diagram and show that the recently introduced occupation-spectrum discontinuity computed from the eigenspectrum of the one-particle density matrix is noticeably smaller in the Luttinger liquid compared to the localized regions. Moreover, we use the functional renormalization group scheme to study the finite-size dependence of the conductance, which also resolves the existence of the Luttinger liquid and is computationally cheap. Our main results concern the finite-energy density case. Using exact diagonalization and by computing various established measures of the many-body localization-delocalization transition, we argue that the zero-temperature Luttinger liquid smoothly evolves into a finite-energy density ergodic phase without any intermediate phase transition.

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Transport in quasiperiodic interacting systems: From superdiffusion to subdiffusion

Cited by 74 publications

References 61 publications

Slow dynamics and strong finite-size effects in many-body localization with random and quasiperiodic potentials

Slow dynamics and strong finite-size effects in many-body localization with random and quasiperiodic potentials

Spin transport in a long-range-interacting spin chain

Many-body localization of spinless fermions with attractive interactions in one dimension

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