Replica-nondiagonal solutions in the SYK model
Open accessAbstract
We study the SYK model in the large N limit beyond the replica-diagonal approximation. First we show that there are exact replica-nondiagonal solutions of the saddle point equations for q = 2 for any finite replica number M.In the interacting q = 4 case we are able to construct the numerical solutions, which are in one-to-one correspondence to the analytic solutions of the quadratic model. These solutions are singular in the M → 0 limit in both quadratic and quartic interaction cases. The calculations of the on-shell action at finite integer M show that the nondiagonal replica-symmetric saddles are subleading in both quadratic and quartic cases. We also study replica-nondiagonal solutions of the SYK in the strong coupling limit. For arbitrary q we show that besides the usual solutions of the replica-diagonal saddle point equations in the conformal limit, there are also replica-nondiagonal solutions for any value of M (including zero). The specific configurations that we study, have factorized time and replica dependencies. The corresponding saddle point equations are separable at strong coupling, and can be solved using the Parisi ansatz from spin glass theory. We construct the solutions which correspond to the replica-symmetric case and to one-step replica symmetry breaking. We compute the regularizized free energy on these solutions in the limit of zero replicas. It is observed that there are nondiagonal solutions with the regularized free energy lower than that of the standard diagonal conformal solution.
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The authors of [39] showed that in a large-coupling (or low-temperature) limit that reduces to an EFT of the low-energy dynamics of SYK, saddles that correlate replicas in the computation of Z_m become dominant both at positive integer m and in the m→0 limit, and therefore lead to a spin glasslike phase transition in this low-energy EFT.
“the authors of [39] showed that in a large-coupling (or low-temperature) limit that reduces to an EFT of the low-energy dynamics of SYK, saddles that correlate replicas in the computation of Z m become dominant both at positive integer m and in the m → 0 limit, and therefore lead to a spin glasslike phase transition in this low-energy EFT.”
From Free energy from replica wormholes (2021) · cites this paper as [39]
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Experimental — accuracy not yet measuredJT gravity is only dual to a low-energy regime of SYK, and an appropriate IR limit of SYK can exhibit a different phase structure than the full SYK system.
“and (ii) JT gravity is only dual to a low-energy regime of SYK, and as shown in [39] an appropriate IR limit of SYK can exhibit a different phase structure than the full SYK system.”
From Free energy from replica wormholes (2021) · cites this paper as [39]
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Cited by
Sorted by citations
Free energy from replica wormholes
Engelhardt, N., Fischetti, S., & Maloney, A. (2021) · Physical Review D · doi:10.1103/physrevd.103.046021 · Cited by 90 · see citing works
Replica symmetry breaking in random matrix model: A toy model of wormhole networks
Okuyama, K. (2020) · Physics Letters B · doi:10.1016/j.physletb.2020.135280 · Cited by 18 · see citing works
- Authors
- Aref’eva, I., Khramtsov, M., Tikhanovskaya, M., & Volovich, I.
- Affiliations
- Russian Academy of Sciences (RU)
- Corresponding author
- Khramtsov, Mikhail
- Venue
- Journal of High Energy Physics
- Published
- 2019-07
- Volume
- 2019
- Issue
- 7
- ISSN
- 1029-8479 (ISSN-L)
- OpenAlex
- W2900442649
- Cited by
- 41
- References
- 6
- Citations by year
- 2025: 1 · 2024: 2 · 2022: 4 · 2021: 7 · 2020: 14 · 2019: 11 · 2018: 2
- FWCI
- 4.67
- Type
- journal article
- Language
- en
- Open access
- diamond
- doi.org
- Licence
- Locations
- Journal of High Energy Physics (publishedVersion, cc-by)
- arXiv (Cornell University) (publishedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- arXiv (Cornell University)
- Funders
- Okinawa Institute of Science and Technology Graduate University
- Russian Science Foundation (17-71-20154)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Keywords
- Sachdev-Ye-Kitaev model, replica symmetry breaking, saddle-point equations, large N limit, quadratic model, quartic interaction, on-shell action, strong coupling limit, Parisi ansatz, one-step replica symmetry breaking, free energy, conformal limit
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