Exact moments of the SachdevYeKitaev model up to order 1/ N ^{2}
Abstract
We analytically evaluate the moments of the spectral density of the qbody SachdevYeKitaev (SYK) model, and obtain order 1/ N ^{2} corrections for all moments, where N is the total number of Majorana fermions. To order 1/ N, moments are given by those of the weight function of the QHermite polynomials. Representing Wick contractions by rooted chord diagrams, we show that the 1/ N ^{2} correction for each chord diagram is proportional to the number of triangular loops of the corresponding intersection graph, with an extra grading factor when q is odd. Therefore the problem of finding 1/ N ^{2} corrections is mapped to a triangle counting problem. Since the total number of triangles is a purely graphtheoretic property, we can compute them for the q = 1 and q = 2 SYK models, where the exact moments can be obtained analytically using other methods, and therefore we have solved the moment problem for any q to 1/ N ^{2} accuracy. The moments are then used to obtain the spectral density of the SYK model to order 1/ N ^{2}. We also obtain an exact analytical result for all contraction diagrams contributing to the moments, which can be evaluated upmore »
 Authors:

 Shanghai Jiao Tong Univ., Shanghai (China)
 Stony Brook Univ., Stony Brook, NY (United States)
 Publication Date:
 Research Org.:
 The State Univ. of New York, Stony Brook, NY (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1505592
 Grant/Contract Number:
 FG0288ER40388
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Volume: 2018; Journal Issue: 4; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 1/N Expansion; Matrix Models; Random Systems
Citation Formats
GarcíaGarcía, Antonio M., Jia, Yiyang, and Verbaarschot, Jacobus J. M. Exact moments of the SachdevYeKitaev model up to order 1/N2. United States: N. p., 2018.
Web. doi:10.1007/jhep04(2018)146.
GarcíaGarcía, Antonio M., Jia, Yiyang, & Verbaarschot, Jacobus J. M. Exact moments of the SachdevYeKitaev model up to order 1/N2. United States. doi:10.1007/jhep04(2018)146.
GarcíaGarcía, Antonio M., Jia, Yiyang, and Verbaarschot, Jacobus J. M. Fri .
"Exact moments of the SachdevYeKitaev model up to order 1/N2". United States. doi:10.1007/jhep04(2018)146. https://www.osti.gov/servlets/purl/1505592.
@article{osti_1505592,
title = {Exact moments of the SachdevYeKitaev model up to order 1/N2},
author = {GarcíaGarcía, Antonio M. and Jia, Yiyang and Verbaarschot, Jacobus J. M.},
abstractNote = {We analytically evaluate the moments of the spectral density of the qbody SachdevYeKitaev (SYK) model, and obtain order 1/N2 corrections for all moments, where N is the total number of Majorana fermions. To order 1/N, moments are given by those of the weight function of the QHermite polynomials. Representing Wick contractions by rooted chord diagrams, we show that the 1/N2 correction for each chord diagram is proportional to the number of triangular loops of the corresponding intersection graph, with an extra grading factor when q is odd. Therefore the problem of finding 1/N2 corrections is mapped to a triangle counting problem. Since the total number of triangles is a purely graphtheoretic property, we can compute them for the q = 1 and q = 2 SYK models, where the exact moments can be obtained analytically using other methods, and therefore we have solved the moment problem for any q to 1/N2 accuracy. The moments are then used to obtain the spectral density of the SYK model to order 1/N2. We also obtain an exact analytical result for all contraction diagrams contributing to the moments, which can be evaluated up to eighth order. This shows that the QHermite approximation is accurate even for small values of N.},
doi = {10.1007/jhep04(2018)146},
journal = {Journal of High Energy Physics (Online)},
issn = {10298479},
number = 4,
volume = 2018,
place = {United States},
year = {2018},
month = {4}
}
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