Power-law out of time order correlation functions in the SYK model

Journal Article · Wed Jun 21 00:00:00 EDT 2017 · Nuclear Physics. B

DOI:https://doi.org/10.1016/j.nuclphysb.2017.06.012· OSTI ID:1366547

Bagrets, Dmitry; Altland, Alexander; Kamenev, Alex

We evaluate the finite temperature partition sum and correlation functions of the Sachdev–Ye–Kitaev (SYK) model. Starting from a recently proposed mapping of the SYK model onto Liouville quantum mechanics, we obtain our results by exact integration over conformal Goldstone modes reparameterizing physical time. Perhaps, the least expected result of our analysis is that at time scales proportional to the number of particles the out of time order correlation function crosses over from a regime of exponential decay to a universal $t^{-6}$ power-law behavior.

• Research Organization: Univ. of Minnesota, Minneapolis, MN (United States); Univ. of Cologne (Germany)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES); German Research Foundation (DFG)
• Grant/Contract Number: FG02-08ER46482; CRC 183
• OSTI ID: 1366547
• Alternate ID(s): OSTI ID: 1467077
• Journal Information: Nuclear Physics. B, Journal Name: Nuclear Physics. B Vol. 921 Journal Issue: C; ISSN 0550-3213
• Publisher: Elsevier
• Country of Publication: Netherlands
• Language: English

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73 NUCLEAR PHYSICS AND RADIATION PHYSICS