Almost conserved operators in nearly many-body localized systems

Pancotti, Nicola; Knap, Michael; Huse, David A.; Cirac, J. I.; Bañuls, Mari Carmen

doi:10.1103/physrevb.97.094206

Cited by 21 publications

(17 citation statements)

References 71 publications

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“…B. This is in some sense the MBL-side mirror image of the slow thermalization rates measured by Pancotti et al 44 on the ETH side of the transition. Pancotti et al characterize the distribution of operator decay rates of the most nearly conserved local operators in terms of extreme value statistics; these anomalously slow decay rates probe the least thermal states on the ETH side of the MBL transitionthose states that take the longest to decay to equilibrium.…”

Section: Discussionsupporting

confidence: 68%

Extracting many-body localization lengths with an imaginary vector potential

2021

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One challenge of studying the many-body localization transition is defining the length scale that diverges upon the transition to the ergodic phase. In this manuscript we explore the localization properties of a ring with onsite disorder subject to an imaginary magnetic flux. We connect the imaginary flux which delocalizes singleparticle orbitals of an Anderson-localized ring with the localization length of an open chain. We thus identify the delocalizing imaginary flux per site with an inverse localization length characterizing the transport properties of the open chain. We put this intuition to use by exploring the phase diagram of a disordered interacting chain, and we find that the inverse imaginary flux per bond provides an accessible description of the transition and its diverging localization length.

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Section: Discussionsupporting

confidence: 68%

Extracting many-body localization lengths with an imaginary vector potential

2021

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“…Nevertheless, full localization persists above a nonzero critical disorder strength . This many-body localized (MBL) phase is characterized by an extensive set of quasilocal integrals of motion (the l-bits) which generalize the diagonal orbitals of the Anderson model to the interacting case [26][27][28][29][30][31][32][33]. The expansion of H in terms of the l-bit operators contains higher-order terms as compared to the Anderson case:…”

Section: A L-bit Basismentioning

confidence: 99%

“…In one dimension d = 1, finite but weak interactions between the particles preserve localization . In such "many-body localized" (MBL) systems, the orbitals are dressed into quasilocal integrals of motion called localized bits (or l-bits) [26][27][28][29][30][31][32][33]. These l-bits underlie the persistent local memory observed in several quantum optical experiments [34][35][36][37][38][39][40][41][42][43].…”

Section: Introductionmentioning

confidence: 99%

Avalanche induced coexisting localized and thermal regions in disordered chains

Crowley

Chandran

2020

Phys. Rev. Research

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We investigate the stability of an Anderson localized chain to the inclusion of a single finite interacting thermal seed. This system models the effects of rare low-disorder regions on many-body localized chains. Above a threshold value of the mean localization length, the seed causes runaway thermalization in which a finite fraction of the orbitals are absorbed into a thermal bubble. This "partially avalanched" regime provides a simple example of a delocalized, nonergodic dynamical phase. We derive the hierarchy of length scales necessary for typical samples to exhibit the avalanche instability, and show that the required seed size diverges at the avalanche threshold. We introduce a dimensionless statistic that measures the effective size of the thermal bubble, and use it to numerically confirm the predictions of avalanche theory in the Anderson chain at infinite temperature.

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“…The MBL-phase in the limit α → ∞ is characterized by the existence of the LIOMs {τ x } 73 which are exponentially localized in space [14][15][16][17][18][19][20]…”

Section: Algebraic Localizationmentioning

confidence: 99%

Algebraic many-body localization and its implications on information propagation

Tomasi

2019

Phys. Rev. B

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We probe the existence of a many-body localized phase (MBL-phase) in a spinless fermionic Hubbard chain with algebraically localized single-particle states, by investigating both static and dynamical properties of the system. This MBL-phase can be characterized by an extensive number of integrals of motion which develop algebraically decaying tails, unlike the case of exponentially localized single-particle states. We focus on the implications for the quantum information propagation through the system. We provide evidence that the bipartite entanglement entropy after a quantum quench has an unbounded algebraic growth in time, while the quantum Fisher information grows logarithmically.

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Almost conserved operators in nearly many-body localized systems

Cited by 21 publications

References 71 publications

Extracting many-body localization lengths with an imaginary vector potential

Extracting many-body localization lengths with an imaginary vector potential

Avalanche induced coexisting localized and thermal regions in disordered chains

Algebraic many-body localization and its implications on information propagation

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