# Disorder in the Sachdev–Ye–Kitaev model

## Abstract

We give qualitative arguments in support of the mesoscopic nature of the Sachdev–Ye–Kitaev (SYK) model in the regime with *q* ^{2}/ *N* << 1 with *N* Majorana particles coupled by antisymmetric and random interactions of range *q*. Using a stochastic deformation of the SYK model, we show that its characteristic determinant obeys a viscid Burgers equation with a small spectral viscosity in the regime with *q*/ *N* = 1/2. In particular, the stochastic evolution of the SYK model can be mapped exactly onto that of random matrix theory, with universal Airy oscillations at the edges.

- Authors:

- Publication Date:

- Research Org.:
- The State Univ. of New York, Stony Brook, NY (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1437728

- Alternate Identifier(s):
- OSTI ID: 1511000

- Grant/Contract Number:
- FG02-88ER40388; DEC-2011/02/A/ST1/00119

- Resource Type:
- Journal Article: Published Article

- Journal Name:
- Physics Letters B

- Additional Journal Information:
- Journal Name: Physics Letters B Journal Volume: 773 Journal Issue: C; Journal ID: ISSN 0370-2693

- Publisher:
- Elsevier

- Country of Publication:
- Netherlands

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

### Citation Formats

```
Liu, Yizhuang, Nowak, Maciej A., and Zahed, Ismail.
```*Disorder in the Sachdev–Ye–Kitaev model*. Netherlands: N. p., 2017.
Web. doi:10.1016/j.physletb.2017.08.054.

```
Liu, Yizhuang, Nowak, Maciej A., & Zahed, Ismail.
```*Disorder in the Sachdev–Ye–Kitaev model*. Netherlands. doi:10.1016/j.physletb.2017.08.054.

```
Liu, Yizhuang, Nowak, Maciej A., and Zahed, Ismail. Sun .
"Disorder in the Sachdev–Ye–Kitaev model". Netherlands. doi:10.1016/j.physletb.2017.08.054.
```

```
@article{osti_1437728,
```

title = {Disorder in the Sachdev–Ye–Kitaev model},

author = {Liu, Yizhuang and Nowak, Maciej A. and Zahed, Ismail},

abstractNote = {We give qualitative arguments in support of the mesoscopic nature of the Sachdev–Ye–Kitaev (SYK) model in the regime with q2/N << 1 with N Majorana particles coupled by antisymmetric and random interactions of range q. Using a stochastic deformation of the SYK model, we show that its characteristic determinant obeys a viscid Burgers equation with a small spectral viscosity in the regime with q/N = 1/2. In particular, the stochastic evolution of the SYK model can be mapped exactly onto that of random matrix theory, with universal Airy oscillations at the edges.},

doi = {10.1016/j.physletb.2017.08.054},

journal = {Physics Letters B},

issn = {0370-2693},

number = C,

volume = 773,

place = {Netherlands},

year = {2017},

month = {10}

}

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Publisher's Version of Record at 10.1016/j.physletb.2017.08.054

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Cited by: 10 works

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#### Figures / Tables:

Fig. 1: Schematic rendering of the spectral form factor for the SYK model as evaluated in [14]. Four mesoscopic regimes are identified. See text.

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Works referencing / citing this record:

##
Three dimensional view of arbitrary q SYK models

journal, February 2018

- Das, Sumit R.; Ghosh, Animik; Jevicki, Antal
- Journal of High Energy Physics, Vol. 2018, Issue 2

##
Three dimensional view of arbitrary q SYK models

journal, February 2018

- Das, Sumit R.; Ghosh, Animik; Jevicki, Antal
- Journal of High Energy Physics, Vol. 2018, Issue 2

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*