Exact moments of the Sachdev-Ye-Kitaev model up to order 1/N2

García-García, Antonio M.; Jia, Yiyang; Verbaarschot, Jacobus J. M.

doi:10.1007/jhep04(2018)146

Title: Exact moments of the Sachdev-Ye-Kitaev model up to order 1/N²

Journal Article · Fri Apr 27 00:00:00 EDT 2018 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep04(2018)146· OSTI ID:1505592

García-García, Antonio M. ^[1]; Jia, Yiyang ^[2];

^[2]

Shanghai Jiao Tong Univ., Shanghai (China)
Stony Brook Univ., Stony Brook, NY (United States)

We analytically evaluate the moments of the spectral density of the q-body Sachdev-Ye-Kitaev (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 Q-Hermite 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 graph-theoretic 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 Q-Hermite approximation is accurate even for small values of N.

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

Sponsoring Organization:: USDOE

Grant/Contract Number:: FG02-88ER40388

OSTI ID:: 1505592

Journal Information:: Journal of High Energy Physics (Online), Vol. 2018, Issue 4; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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