Universal Properties of Many-Body Localization Transitions in Quasiperiodic Systems

Zhang, Shixin; Yao, Hong

doi:10.1103/physrevlett.121.206601

Cited by 82 publications

(70 citation statements)

References 68 publications

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“…We also find possible indications of the breakdown of powerlaw behavior in larger systems: the decay becomes faster than a power law with increasing time. Our findings are consistent with the aforementioned predictions of Khemani et al concerning two different universality classes for the MBL transitions with random and quasi-periodic potentials [23] (see also the related study [28]).…”

Section: Introductionsupporting

confidence: 94%

Many-body delocalization dynamics in long Aubry-André quasiperiodic chains

Doggen

Mirlin

2019

Phys. Rev. B

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We study quench dynamics in an interacting spin chain with a quasi-periodic on-site field, known as the interacting Aubry-André model of many-body localization. Using the time-dependent variational principle, we assess the late-time behavior for chains up to L = 50. We find that the choice of periodicity Φ of the quasi-periodic field influences the dynamics. For Φ = ( √ 5 − 1)/2 (the inverse golden ratio) and interaction ∆ = 1, the model most frequently considered in the literature, we obtain the critical disorder Wc = 4.8 ± 0.5 in units where the non-interacting transition is at W = 2. At the same time, for periodicity Φ = √ 2/2 we obtain a considerably higher critical value, Wc = 7.8 ± 0.5. Finite-size effects on the critical disorder Wc are much weaker than in the purely random case. This supports the enhancement of Wc in the case of a purely random potential by rare "ergodic spots," which do not occur in the quasi-periodic case. Further, the data suggest that the decay of the antiferromagnetic order in the delocalized phase is faster than a power law. arXiv:1901.06971v5 [cond-mat.dis-nn]

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Section: Introductionsupporting

confidence: 94%

Many-body delocalization dynamics in long Aubry-André quasiperiodic chains

Doggen

Mirlin

2019

Phys. Rev. B

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“…This transition describes a breakdown of equilibrium statistical mechanics and has many features that distinguish it from phase transitions usually encountered in either quantum or equilibrium classical systems. Despite focused efforts in studying this transition, 19,[29][30][31][32][33][34][35][36][37][38][39][40][41] the combination of finite energy density, interactions and disorder remains a challenge to all known theoretical and computational techniques. Much of the insight into the existence of the MBL phase and transition have been obtained by exact diagonalization studies, performed on small system sizes (L 30).…”

Section: Introductionmentioning

confidence: 99%

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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“…This is a well-known problem for the finite-size scaling analysis of the MBL transition. For the MBL transition in models with short-range interactions, the critical exponent ν extracted from finite-size scaling is about ν = 0.91 ± 0.07 or 0.80 ± 0.04 (for gap statistics or entanglement entropy, up to L = 22 [12]) or ν = 1.09 (for entanglement entropy, up to L = 18 [14]), which is much smaller than the prediction of ν = 3.1±0.3 obtained from the real-space renormalization group analysis [19,20]. The latter satisfies the Harris/CCFS/CLO bound.…”

Section: Finite-size Scalingmentioning

confidence: 58%

“…To date, there are a number of techniques developed to understand MBL, including analytic calculations [9], numerically exact diagonalization [8,[10][11][12][13][14], renormalization group approaches such as the excited-state realspace renormalization group and density matrix renormalization groups (DMRG and its time-dependent version tDMRG) [15][16][17][18][19][20], and perturbation methods such as Born approximation [21] and self-consistent theories [22]. Recently, a renormalization flow technique, namely the Wegner-Wilson flow renormalization, has also been applied to investigate the MBL phase transition [23].…”

Section: Introductionmentioning

confidence: 99%

Many-body localization in XY spin chains with long-range interactions: An exact-diagonalization study

et al. 2019

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We investigate the transition from the many-body localized phase to the ergodic thermalized phase at an infinite temperature in an XY spin chain with L spins, which experiences power-law decaying interactions in the form of Vij ∝ 1/ |i − j| α (i, j = 1, · · · , L) and a random transverse field. By performing large-scale exact diagonalization for the chain size up to L = 18, we systematically analyze the energy gap statistics, half-chain entanglement entropy, and uncertainty of the entanglement entropy of the system at different interaction exponents α. The finite-size critical scaling allows us to determine the critical disorder strength Wc and critical exponent ν at the many-body localization phase transition, as a function of the interaction exponent α in the limit L → ∞. We find that both Wc and ν diverge when α decreases to a critical power αc 1.16 ± 0.17, indicating the absence of many-body localization for α < αc. Our result is useful to resolve the contradiction on the critical power found in two previous studies, αc = 3/2 from scaling argument in Phys. Rev. B 92, 104428 (2015) and αc ≈ 1 from quantum dynamics simulation in Phys. Rev. A 99, 033610 (2019). arXiv:1908.04031v2 [cond-mat.quant-gas]

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Universal Properties of Many-Body Localization Transitions in Quasiperiodic Systems

Cited by 82 publications

References 68 publications

Many-body delocalization dynamics in long Aubry-André quasiperiodic chains

Many-body delocalization dynamics in long Aubry-André quasiperiodic chains

Kosterlitz-Thouless scaling at many-body localization phase transitions

Many-body localization in XY spin chains with long-range interactions: An exact-diagonalization study

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