# 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:
- 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},

number = [C],

volume = [773],

place = {Netherlands},

year = {2017},

month = {10}

}

Free Publicly Available Full Text

Publisher's Version of Record

DOI: 10.1016/j.physletb.2017.08.054

DOI: 10.1016/j.physletb.2017.08.054

Other availability

Cited by: 10 works

*Citation information provided by*

Web of Science

Web of Science

#### 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.

All figures and tables
(1 total)

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.

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