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Title: 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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1016/j.physletb.2017.08.054

Citation Metrics:
Cited by: 10 works
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Figures / Tables:

Fig. 1 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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