Abstract
The SYK model consists of N ≫ 1 fermions in 0 + 1 dimensions with a random, all-to-all quartic interaction. Recently, Kitaev has found that the SYK model is maximally chaotic and has proposed it as a model of holography. We solve the SchwingerDyson equation and compute the spectrum of two-particle states in SYK, finding both a continuous and discrete tower. The four-point function is expressed as a sum over the spectrum. The sum over the discrete tower is evaluated.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Kitaev, A simple model of quantum holography, in KITP strings seminar and Entanglement 2015 program, http://online.kitp.ucsb.edu/online/entangled15/, UC Santa Barbara, Santa Barbara U.S.A. February 12, April 7 and May 27 2015.
S. Sachdev and J.-W. Ye, Gapless spin fluid ground state in a random, quantum Heisenberg magnet, Phys. Rev. Lett. 70 (1993) 3339 [cond-mat/9212030] [INSPIRE].
A. Larkin and Y.N. Ovchinnikov, Quasiclassical method in the theory of superconductivity, Sov. Phys. JETP 28 (1969) 1200.
A. Kitaev, Hidden correlations in the Hawking radiation and thermal noise, talk given at Fundamental Physics Prize Symposium, November 10 2014.
S.H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 03 (2014) 067 [arXiv:1306.0622] [INSPIRE].
S.H. Shenker and D. Stanford, Stringy effects in scrambling, JHEP 05 (2015) 132 [arXiv:1412.6087] [INSPIRE].
J. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, arXiv:1503.01409 [INSPIRE].
O. Parcollet and A. Georges, Non-Fermi-liquid regime of a doped Mott insulator, Phys. Rev. B 59 (1999) 5341 [cond-mat/9806119].
S. Sachdev, Holographic metals and the fractionalized Fermi liquid, Phys. Rev. Lett. 105 (2010) 151602 [arXiv:1006.3794] [INSPIRE].
S. Sachdev, Strange metals and the AdS/CFT correspondence, J. Stat. Mech. 11 (2010) P11022 [arXiv:1010.0682] [INSPIRE].
S.H. Shenker and D. Stanford, Multiple shocks, JHEP 12 (2014) 046 [arXiv:1312.3296] [INSPIRE].
J. Maldacena and D. Stanford, to appear.
A. Kitaev, to appear.
S. Sachdev, Bekenstein-Hawking entropy and strange metals, Phys. Rev. X 5 (2015) 041025 [arXiv:1506.05111] [INSPIRE].
A.J. Bray and M.A. Moore, Replica theory of quantum spin glasses, J. Phys. C 13 (1980) L655.
A. Georges, O. Parcollet and S. Sachdev, Mean field theory of a quantum Heisenberg spin glass, Phys. Rev. Lett. 85 (2000) 840 [cond-mat/9909239].
A. Kitaev, private communication.
J.M. Maldacena, J. Michelson and A. Strominger, Anti-de Sitter fragmentation, JHEP 02 (1999) 011 [hep-th/9812073] [INSPIRE].
A. Almheiri and J. Polchinski, Models of AdS 2 backreaction and holography, JHEP 11 (2015) 014 [arXiv:1402.6334] [INSPIRE].
D.A. Roberts and D. Stanford, Two-dimensional conformal field theory and the butterfly effect, Phys. Rev. Lett. 115 (2015) 131603 [arXiv:1412.5123] [INSPIRE].
D.A. Roberts, D. Stanford and L. Susskind, Localized shocks, JHEP 03 (2015) 051 [arXiv:1409.8180] [INSPIRE].
P. Hosur, X.-L. Qi, D.A. Roberts and B. Yoshida, Chaos in quantum channels, JHEP 02 (2016) 004 [arXiv:1511.04021] [INSPIRE].
G. Gur-Ari, M. Hanada and S.H. Shenker, Chaos in classical D0-brane mechanics, JHEP 02 (2016) 091 [arXiv:1512.00019] [INSPIRE].
D. Stanford, Many-body chaos at weak coupling, arXiv:1512.07687 [INSPIRE].
J. Polchinski, Chaos in the black hole S-matrix, arXiv:1505.08108 [INSPIRE].
R. Haag, Local quantum physics: fields, particles, algebras, Springer, Berlin Germany (1992).
T. Hartman, S. Jain and S. Kundu, Causality constraints in conformal field theory, arXiv:1509.00014 [INSPIRE].
I. Gradshteyn and I. Ryzhik, Table of integrals, series and products, 5th ed., Academic Press, U.S.A. (1994).
G. Watson, A treatise on the theory of Bessel functions, Cambridge University Press, Cambridge U.K. (1944).
N.M. Temme, Special functions, an introduction to the classical functions of mathematical physics, John Wiley & Sons Inc., U.S.A. (1996).
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: 1601.06768
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, 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 license, and indicate if changes were made.
About this article
Cite this article
Polchinski, J., Rosenhaus, V. The spectrum in the Sachdev-Ye-Kitaev model. J. High Energ. Phys. 2016, 1 (2016). https://doi.org/10.1007/JHEP04(2016)001
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2016)001