Multiscale entanglement clusters at the many-body localization phase transition

Herviou, Loïc; Bera, Soumya; Bardarson, Jens H.

doi:10.1103/physrevb.99.134205

Cited by 54 publications

(46 citation statements)

References 83 publications

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“…Many approximate RG studies [2,36,37,39] and one recent ED study [31] of the MBL transition seem to agree on the prediction that physical lengths of thermal inclusions in critical systems are distributed according to a power law ∝ (L T ) −α , with the exponent taking an apparently universal value near α = 2. In addition, and consistent with a KT-type scenario, is the possibility of an intermediate critical MBL phase [39] where the lengths of thermal inclusions are power-law distributed with a continuously varying exponent [2,31,39].…”

Section: Distribution Of Thermal Inclusionsmentioning

confidence: 76%

Renormalization-group study of the many-body localization transition in one dimension

Morningstar

Huse

2019

Phys. Rev. B

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Using a new approximate strong-randomness renormalization group (RG), we study the manybody localized (MBL) phase and phase transition in one-dimensional quantum systems with shortrange interactions and quenched disorder. Our RG is built on those of Zhang et al.[1] and Goremykina et al. [2], which are based on thermal and insulating blocks. Our main addition is to characterize each insulating block with two lengths: a physical length, and an internal decay length ζ for its effective interactions. In this approach, the MBL phase is governed by a RG fixed line that is parametrized by a global decay lengthζ, and the rare large thermal inclusions within the MBL phase have a fractal geometry. As the phase transition is approached from within the MBL phase,ζ approaches the finite critical value corresponding to the avalanche instability, and the fractal dimension of large thermal inclusions approaches zero. Our analysis is consistent with a Kosterlitz-Thouless-like RG flow, with no intermediate critical MBL phase. arXiv:1903.02001v4 [cond-mat.stat-mech]

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Section: Distribution Of Thermal Inclusionsmentioning

confidence: 76%

Renormalization-group study of the many-body localization transition in one dimension

Morningstar

Huse

2019

Phys. Rev. B

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“…We also note, that a very recent exact diagonalization results appear to be consistent with the KT prediction of algebraic behavior of thermal cluster distributions within the MBL phase, with an exponent α c ≈ 2 at criticality. 82 Finally, we note that the link with the behavior of thermal Griffiths regions suggests that it is possible, at least in principle, to extract this exponent experimentally. We can imagine a cold atom setup where the system is quenched into the MBL regime from an initial configuration with a local 'imbalance' (period-two density modulation).…”

Section: Discussion and Outlookmentioning

confidence: 89%

Kosterlitz-Thouless scaling at many-body localization phase transitions

et al. 2019

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We propose a scaling theory for the many-body localization (MBL) phase transition in one dimension, building on the idea that it proceeds via a 'quantum avalanche'. We argue that the critical properties can be captured at a coarse-grained level by a Kosterlitz-Thouless (KT) renormalization group (RG) flow. On phenomenological grounds, we identify the scaling variables as the density of thermal regions and the lengthscale that controls the decay of typical matrix elements. Within this KT picture, the MBL phase is a line of fixed points that terminates at the delocalization transition. We discuss two possible scenarios distinguished by the distribution of rare, fractal thermal inclusions within the MBL phase. In the first scenario, these regions have a stretched exponential distribution in the MBL phase. In the second scenario, the near-critical MBL phase hosts rare thermal regions that are power-law distributed in size. This points to the existence of a second transition within the MBL phase, at which these power-laws change to the stretched exponential form expected at strong disorder. We numerically simulate two different phenomenological RGs previously proposed to describe the MBL transition. Both RGs display a universal power-law length distribution of thermal regions at the transition with a critical exponent αc = 2, and continuously varying exponents in the MBL phase consistent with the KT picture. arXiv:1811.03103v3 [cond-mat.dis-nn]

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“…The investigation of the transition between MBL and ergodic dynamics may also benefit in the future from quantum computation. It is notoriously difficult to study numerically due to the requirement of large systems and/or long-time simulations [88][89][90].…”

Section: Discussionmentioning

confidence: 99%

Simulating quantum many-body dynamics on a current digital quantum computer

et al. 2019

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Universal quantum computers are potentially an ideal setting for simulating many-body quantum dynamics that is out of reach for classical digital computers. We use state-of-the-art IBM quantum computers to study paradigmatic examples of condensed matter physics -we simulate the effects of disorder and interactions on quantum particle transport, as well as correlation and entanglement spreading. Our benchmark results show that the quality of the current machines is below what is necessary for quantitatively accurate continuous time dynamics of observables and reachable system sizes are small comparable to exact diagonalization. Despite this, we are successfully able to demonstrate clear qualitative behaviour associated with localization physics and many-body interaction effects.IBM is not alone in their efforts to make quantum computing more mainstream, with Microsoft introducing the Q-sharp programming language [53], Google developing the Circq python library [54], and Rigetti providing their own Quantum Cloud Service and Forest SDK built on Python [55]. Rigetti

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Multiscale entanglement clusters at the many-body localization phase transition

Cited by 54 publications

References 83 publications

Renormalization-group study of the many-body localization transition in one dimension

Renormalization-group study of the many-body localization transition in one dimension

Kosterlitz-Thouless scaling at many-body localization phase transitions

Simulating quantum many-body dynamics on a current digital quantum computer

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