Exact moments of the Sachdev-Ye-Kitaev model up to order 1/N 2

Exact moments of the Sachdev-Ye-Kitaev model up to order 1/N 2

Blog Article

Abstract We analytically evaluate the moments of the spectral density of the q-body Sachdev-Ye-Kitaev (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 Q-Hermite Hair Bands 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 graph-theoretic property, we can compute them for the q = 1 and q = 2 SYK models, where the exact moments can be Voltage Tester 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 up to eighth order.This shows that the Q-Hermite approximation is accurate even for small values of N.