Sachdev–Ye–Kitaev model as Liouville quantum mechanics

By Dmitry Bagrets, A. Altland, Alex Kamenev. 2016

315 citations recorded by the source corpus.

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 ≫ N ln ⁡ 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 ϵ 1 / 2 . We also present exact diagonalization study supporting our conclusions.

Subfields: Condensed Matter Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/84240f6444581e10f848785bb3542be342f15358

How researchers see this paper

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In Condensed Matter Physics

1. E. Witten
2. D. Stanford
3. Alexei Y. Kitaev
4. Tom Mertens
5. G. Turiaci
6. S. J. Suh
7. Zhenbin Yang
8. H. Verlinde

In Statistical and Nonlinear Physics

1. D. Stanford
2. Phil Saad
3. Zhenbin Yang
4. E. Witten
5. Jordan S. Cotler
6. S. Shenker
7. K. Jensen
8. G. Turiaci

Citations in the corpus

• Power-law out of time order correlation functions in the SYK model (2017, methodology): “[21] we introduced a method to isolate these fluctuations and perform a full integration over the Goldstone mode manifold.”
• Fermionic localization of the schwarzian theory (2017, background): “If we pick a local gauge condition, like φ(0) = 0, φ′(0) = 1, φ′′(0) = 0, then the measure actually turns out to be local, and equal to the measure on diff(S(1))/SL(2,R) inherited from the measure on diff(S(1)) discussed in [10]:”
• The quantum gravity dynamics of near extremal black holes (2018, background): “So, at large time we have a universal power law decay pointed out in [4].”
• Statistical mechanics of a two-dimensional black hole (2018, methodology): “The method of [11, 12] corresponds to fixing one of the points, (φ0, ζ0) = (−π, 1), and using the variable φ = − ln(−χ) + const.”
• Black holes and random matrices (2016, background): “ions of SYK have been constructed in [23,24]. A supersymmetric generalization of the model has been constructed in [25]. A multi avor version has been constructed in [26]. Other related work includes [27,28,29,30]. 5Another discussion of random matrices in black hole physics is [34]. Recent discussi”
• Solving the Schwarzian via the conformal bootstrap (2017, methodology): “take the zero-temperature limit !1. In this limit, our two-point function reduces to G1 ‘ (˝1;˝2) = Z dk2 sinh(2ˇk)e j˝ k2 2(‘+ ik) 2(‘ ik) 2ˇ2 (2 ‘) ; (4.11) which coincides with the result found in [21].14 For the case ‘= 1 we can go further, since we know that the next-to-leading order term 13The”
• Eternal traversable wormhole (2018, background): “36) was already shown to describe correctly the TFD (for η = 0) [30, 31, 32].”
• Low-dimensional de Sitter quantum gravity (2019, methodology): “Stanford and Witten [44] showed that the gauge-fixed measure is local away from θ = 0, given by ∏ θ>0 dφ(θ) φ′(θ) (this measure was used in previous work [45] on the Schwarzian path integral) by explicit computation.”
• Coadjoint orbit action of Virasoro group and two-dimensional quantum gravity dual to SYK/tensor models (2017, background): “One-dimensional Liouville equation of motion has appeared in [13, 18, 47] in the context of boundary dynamics.”