Universal Properties of Many-Body Delocalization Transitions

Potter, Andrew C.; Vasseur, Romain; Parameswaran, S. A.

doi:10.1103/physrevx.5.031033

Cited by 344 publications

(512 citation statements)

References 37 publications

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“…The above arguments suggest that near the MBL phase transition z varies continuously as z = ξ/ζ and hence diverges together with ξ at the critical point. This conclusion is supported by the renormalization group treatments [58,67], which also suggest, as does numerical work [34], that transport through a critical region of size R 0 occurs on a timescale t(R 0 ) ∼ exp(R 0 /ζ c ).…”

Section: Counting Inclusions: the Role Of Dimensionalitymentioning

confidence: 63%

“…An interesting conclusion of Ref. [108], supported by their numerical data, is that the dominant entangling inclusions near the MBL transition are "sparse" [67] and unable to fully thermalize their surroundings, and they are state-dependent. This is rather distinct from the picture developed in the preceding discussion, but the regime being studied is more the finite-size critical regime rather than the Griffiths regimes of the two phases.…”

Section: Numerical Evidencementioning

confidence: 93%

“…The definition of Griffiths regions in a system close to the MBL critical point requires more care. In this regime, even the thermal bulk only appears thermal when probed on lengths scales larger than the correlation length ξ , expected to diverge at the critical point, and on timescales that are long compared with its correlation time τ (ξ ) [which is thought to go as exp(ξ/ζ ) [58,67]]. Hence the boundary between the Griffiths region and the thermal bulk is smeared over the scale ξ and for isolated Griffiths regions to be well defined they must be of size R 0 ξ .…”

Section: Response Of a Single Inclusionmentioning

confidence: 99%

“…Thus, the construction of the MBL critical point is similar to an iterated version of the Griffiths analyses we have gone through here. This is the basic idea underlying the strong-randomness renormalization-group treatments of the MBL transition [58,67,100].…”

Section: Relation To Theories Of the Mbl Transitionmentioning

confidence: 99%

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Rare‐region effects and dynamics near the many‐body localization transition

et al. 2017

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The low-frequency response of systems near the many-body localization phase transition, on either side of the transition, is dominated by contributions from rare regions that are locally "in the other phase", i.e., rare localized regions in a system that is typically thermal, or rare thermal regions in a system that is typically localized. Rare localized regions affect the properties of the thermal phase, especially in one dimension, by acting as bottlenecks for transport and the growth of entanglement, whereas rare thermal regions in the localized phase act as local "baths" and dominate the low-frequency response of the MBL phase. We review recent progress in understanding these rare-region effects, and discuss some of the open questions associated with them: in particular, whether and in what circumstances a single rare thermal region can destabilize the many-body localized phase.

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Section: Counting Inclusions: the Role Of Dimensionalitymentioning

confidence: 63%

Section: Numerical Evidencementioning

confidence: 93%

Section: Response Of a Single Inclusionmentioning

confidence: 99%

Section: Relation To Theories Of the Mbl Transitionmentioning

confidence: 99%

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Rare‐region effects and dynamics near the many‐body localization transition

et al. 2017

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“…[8] has characterized the transition using ground state properties of the disordered Heisenberg chain via a neural network-based approach of classifying entanglement spectra). For a specific disorder configuration, this allows, for instance, to trace the evolution of individual ETH states deep in the MBL regime [40,[46][47][48]. We achieve this by considering the spectra from multiple real-space entanglement cuts as input for the (7) trained with cost function (8) on entanglement spectra obtained from an exact diagonalization on N = 16 sites.…”

Section: Introductionmentioning

confidence: 99%

Probing many-body localization with neural networks

2017

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We show that a simple artificial neural network trained on entanglement spectra of individual states of a many-body quantum system can be used to determine the transition between a many-body localized and a thermalizing regime. Specifically, we study the Heisenberg spin-1/2 chain in a random external field. We employ a multilayer perceptron with a single hidden layer, which is trained on labeled entanglement spectra pertaining to the fully localized and fully thermal regimes. We then apply this network to classify spectra belonging to states in the transition region. For training, we use a cost function that contains, in addition to the usual error and regularization parts, a term that favors a confident classification of the transition region states. The resulting phase diagram is in good agreement with the one obtained by more conventional methods and can be computed for small systems. In particular, the neural network outperforms conventional methods in classifying individual eigenstates pertaining to a single disorder realization. It allows us to map out the structure of these eigenstates across the transition with spatial resolution. Furthermore, we analyze the network operation using the dreaming technique to show that the neural network correctly learns by itself the power-law structure of the entanglement spectra in the many-body localized regime.

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Many body localized systems weakly coupled to baths

Nandkishore

Gopalakrishnan

2016

Annalen der Physik

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We consider what happens when a many body localized system is coupled to a heat bath. Unlike previous works, we do not restrict ourselves to the limit where the bath is large and effectively Markovian, nor to the limit where back action on the bath is negligible. We identify limits where the effect of the bath can be captured by classical noise, and limits where it cannot. We also identify limits in which the bath delocalizes the system, as well as limits in which the system localizes the bath. Using general arguments and dimensional analysis, we constrain the overall phase diagram of the coupled system and bath. Our analysis incorporates all the previously discussed regimes, and also uncovers a new intrinsically quantum regime that has not hitherto been discussed. We discuss baths that are themselves near a localization transition, or are strongly disordered but protected against localization by symmetry or topology. We also discuss situations where the system and bath have different dimensionality (the case of 'boundary MBL' and 'boundary baths').

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Universal Properties of Many-Body Delocalization Transitions

Cited by 344 publications

References 37 publications

Rare‐region effects and dynamics near the many‐body localization transition

Rare‐region effects and dynamics near the many‐body localization transition

Probing many-body localization with neural networks

Many body localized systems weakly coupled to baths

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