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

## Abstract

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.

- Authors:

- Publication Date:

- Research Org.:
- Univ. of Minnesota, Minneapolis, MN (United States); Univ. of Cologne (Germany)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); German Research Foundation (DFG)

- OSTI Identifier:
- 1366547

- Alternate Identifier(s):
- OSTI ID: 1467077

- Grant/Contract Number:
- FG02-08ER46482; CRC 183

- Resource Type:
- Published Article

- Journal Name:
- Nuclear Physics. B

- Additional Journal Information:
- Journal Name: Nuclear Physics. B Journal Volume: 921 Journal Issue: C; Journal ID: ISSN 0550-3213

- Publisher:
- Elsevier

- Country of Publication:
- Netherlands

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

### Citation Formats

```
Bagrets, Dmitry, Altland, Alexander, and Kamenev, Alex. Power-law out of time order correlation functions in the SYK model. Netherlands: N. p., 2017.
Web. doi:10.1016/j.nuclphysb.2017.06.012.
```

```
Bagrets, Dmitry, Altland, Alexander, & Kamenev, Alex. Power-law out of time order correlation functions in the SYK model. Netherlands. doi:10.1016/j.nuclphysb.2017.06.012.
```

```
Bagrets, Dmitry, Altland, Alexander, and Kamenev, Alex. Wed .
"Power-law out of time order correlation functions in the SYK model". Netherlands. doi:10.1016/j.nuclphysb.2017.06.012.
```

```
@article{osti_1366547,
```

title = {Power-law out of time order correlation functions in the SYK model},

author = {Bagrets, Dmitry and Altland, Alexander and Kamenev, Alex},

abstractNote = {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.},

doi = {10.1016/j.nuclphysb.2017.06.012},

journal = {Nuclear Physics. B},

number = C,

volume = 921,

place = {Netherlands},

year = {2017},

month = {6}

}

Free Publicly Available Full Text

Publisher's Version of Record

DOI: 10.1016/j.nuclphysb.2017.06.012

DOI: 10.1016/j.nuclphysb.2017.06.012

Other availability

Cited by: 35 works

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