Abstract
This paper considers a type of generalized large q SYK models which include multi-body interactions between Majorana fermions. We derive an effective action in the limit of large N and large q (with \( \frac{q^2}{N} \) small), and find a universal expression for thermody-namical quantities. We also consider the chaos exponent using the retarded kernel method and find an efficient way to calculate the Lyapunov exponent for generalized large q SYK models numerically.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Sachdev and J. Ye, Gapless spin fluid ground state in a random, quantum Heisenberg magnet, Phys. Rev. Lett.70 (1993) 3339 [cond-mat/9212030] [INSPIRE].
A. Kitaev, A simple model of quantum holography, talks given at KITP, April 7 and May 27 (2015).
A. Kitaev and S.J. Suh, The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual, JHEP05 (2018) 183 [arXiv:1711.08467] [INSPIRE].
J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev.D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].
R. Jackiw, Lower dimensional gravity, Nucl. Phys.B 252 (1985) 343 [INSPIRE].
C. Teitelboim, Gravitation and Hamiltonian structure in two space-time dimensions, Phys. Lett.B 126 (1983) 41.
A. Almheiri and J. Polchinski, Models of AdS 2backreaction and holography, JHEP11 (2015) 014 [arXiv:1402.6334] [INSPIRE].
J. Maldacena, D. Stanford and Z. Yang, Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space, PTEP2016 (2016) 12C104 [arXiv:1606.01857] [INSPIRE].
K. Jensen, Chaos in AdS 2holography, Phys. Rev. Lett.117 (2016) 111601 [arXiv:1605.06098] [INSPIRE].
J. Engelsöy, T.G. Mertens and H. Verlinde, An investigation of AdS 2backreaction and holography, JHEP07 (2016) 139 [arXiv:1606.03438] [INSPIRE].
P. Saad, S.H. Shenker and D. Stanford, JT gravity as a matrix integral, arXiv:1903.11115 [INSPIRE].
J.S. Cotler et al., Black holes and random matrices, JHEP05 (2017) 118 [Erratum ibid.09 (2018) 002] [arXiv:1611.04650] [INSPIRE].
L. Erdős and D. Schröder, Phase transition in the density of states of quantum spin glasses, Math. Phys. Anal. Geom.17 (2014) 441 [arXiv:1407.1552] [INSPIRE].
M. Berkooz, M. Isachenkov, V. Narovlansky and G. Torrents, Towards a full solution of the large N double-scaled SYK model, JHEP03 (2019) 079 [arXiv:1811.02584] [INSPIRE].
X.-L. Qi and A. Streicher, Quantum epidemiology: operator growth, thermal effects and SYK, arXiv:1810.11958 [INSPIRE].
Z. Bi et al., Instability of the non-Fermi liquid state of the Sachdev-Ye-Kitaev model, Phys. Rev.B 95 (2017) 205105 [arXiv:1701.07081] [INSPIRE].
X. Chen et al., Competition between chaotic and nonchaotic phases in a quadratically coupled Sachdev-Ye-Kitaev model, Phys. Rev. Lett.119 (2017) 207603 [arXiv:1705.03406] [INSPIRE].
H.W. Lin, J. Maldacena and Y. Zhao, Symmetries near the horizon, arXiv:1904.12820 [INSPIRE].
L. Susskind, Complexity and Newton’s laws, arXiv:1904.12819 [INSPIRE].
J. Maldacena and X.-L. Qi, Eternal traversable wormhole, arXiv:1804.00491 [INSPIRE].
J. Maldacena, D. Stanford and Z. Yang, Diving into traversable wormholes, Fortsch. Phys.65 (2017) 1700034 [arXiv:1704.05333] [INSPIRE].
P. Gao, D.L. Jafferis and A. Wall, Traversable wormholes via a double trace deformation, JHEP12 (2017) 151 [arXiv:1608.05687] [INSPIRE].
Y. Chen and P. Zhang, Entanglement Entropy of Two Coupled SYK Models and Eternal Traversable Wormhole, JHEP07 (2019) 033 [arXiv:1903.10532] [INSPIRE].
G. Tarnopolsky, Large q expansion in the Sachdev-Ye-Kitaev model, Phys. Rev.D 99 (2019) 026010 [arXiv:1801.06871] [INSPIRE].
J. Maldacena, G.J. Turiaci and Z. Yang, Two dimensional nearly de Sitter gravity, arXiv:1904.01911 [INSPIRE].
D.J. Gross and V. Rosenhaus, A generalization of Sachdev-Ye-Kitaev, JHEP02 (2017) 093 [arXiv:1610.01569] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1905.00811
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Jiang, J., Yang, Z. Thermodynamics and many body chaos for generalized large q SYK models. J. High Energ. Phys. 2019, 19 (2019). https://doi.org/10.1007/JHEP08(2019)019
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2019)019