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Cited by 301Quantum many-body systemsBlack Holes and Theoretical PhysicsQuantum chaos and dynamical systems

Sachdev–Ye–Kitaev model as Liouville quantum mechanics

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Bagrets, Dmitry, Altland, Alexander, Kamenev, Alex·2016·Nuclear Physics B
DOI 10.1016/j.nuclphysb.2016.08.002
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Abstract

We show that the proper inclusion of soft reparameterization modes in the Sachdev–Ye–Kitaev model of N randomly interacting Majorana fermions reduces its long-time behavior to that of Liouville quantum mechanics. As a result, all zero temperature correlation functions decay with the universal exponent ∝τ−3/2 for times larger than the inverse single particle level spacing τ≫Nln⁡N. In the particular case of the single particle Green function this behavior is manifestation of the zero-bias anomaly, or scaling in energy as ϵ1/2. We also present exact diagonalization study supporting our conclusions.

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Crossref · 10.1016/j.nuclphysb.2016.08.002

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  • Recent studies show that SYK does not exhibit a spin glass phase; a saddle-point analysis of the replica trick in the large-N limit indicates that no saddles correlating different replicas dominate the correlators Z^m at any temperature.

    “These investigations show that SYK does not exhibit a spin glass phase; that is, a saddle-point analysis of the replica trick in the large-N limit (see e.g.[33,34]) indicates that no saddles correlating different replicas dominate the correlators Z m at any temperature [33,[35][36][37][38][39][40][41][42][43].”

    From Free energy from replica wormholes (2021) · cites this paper as [33]

    In §2, Preliminaries (pp. 2–3), the paper develops a replica-diagonal large-N saddle and says fluctuations away from it appear to play a lesser role. But it limits its inference that the replica index does not matter to energies above the inverse many-body level spacing and then ignores replica structure; it does not establish the absence of a spin-glass phase or rule out dominant inter-replica saddles in Z^m at every temperature. (LLM, conf=0.83)

    Experimental — accuracy not yet measured

  • Under quite general conditions, a power-law decay holds.

    “Under quite general conditions, a power-law decay holds, as has been demonstrated in single-particle [23], few-body [30] and many-body systems [25, 31-33].”

    From Scrambling the spectral form factor: Unitarity constraints and exact results (2017) · cites this paper as [32]

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Research works printed but not linked: 1

  1. [15][15] Y. V. Nazarov, Y. M. Blanter, Quantum Transport , Cambridge University Press, 2009. -

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Related

Authors
Bagrets, D., Altland, A., & Kamenev, A.
Affiliations
  • University of Cologne (DE)
  • University of Minnesota (US)
Corresponding author
Bagrets, Dmitry
ORCID
Venue
Nuclear Physics B
Publisher
Elsevier BV
Published
2016-10
Volume
911
Pages
191-205
ISSN
0550-3213 (ISSN-L)
DOI
10.1016/j.nuclphysb.2016.08.002
OpenAlex
W2468247974
Cited by
301
References
16
Citations by year
2026: 9 · 2025: 12 · 2024: 12 · 2023: 28 · 2022: 47 · 2021: 35 · 2020: 39 · 2019: 46 · 2018: 39 · 2017: 33 · 2016: 1
FWCI
18.77
Type
journal article
Language
en
Open access
Licence
Locations
  • Nuclear Physics B (publishedVersion, cc-by)
  • Kölner Universitäts PublikationsServer (Universität zu Köln) (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • DOE (DEFG02-08ER46482)
  • QM2–Quantum Matter and Materials of Cologne University
  • Deutsche Forschungsgemeinschaft (CRC 183)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Quantum chaos and dynamical systems
Keywords
Sachdev-Ye-Kitaev model, long-time tails, correlation function decay, zero-bias anomaly, single-particle Green function, level spacing, exact diagonalization

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