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.
Bibliographical noteFunding Information:
We thank J. Verbaarschot and A.M. Garc?a-Garc?a for discussions and for sharing unpublished numerical data. A.K. was supported by DOE contract DEFG02-08ER46482, and acknowledges support by QM2 ? Quantum Matter and Materials of Cologne University. Work supported by CRC 183 of the Deutsche Forschungsgemeinschaft (project A03).