Remarks on the SachdevYeKitaev model
Abstract
We study a quantummechanical model proposed by Sachdev, Ye and Kitaev. The model consists of N Majorana fermions with random interactions of a few fermions at a time. It it tractable in the largeN limit, where the classical variable is a bilocal fermion bilinear. The model becomes strongly interacting at low energies where it develops an emergent conformal symmetry. We study two and fourpoint functions of the fundamental fermions. This provides the spectrum of physical excitations for the bilocal field. The emergent conformal symmetry is a reparametrization symmetry, which is spontaneously broken to S L (2 ,R ) , leading to zero modes. These zero modes are lifted by a small residual explicit breaking, which produces an enhanced contribution to the fourpoint function. This contribution displays a maximal Lyapunov exponent in the chaos region (outoftimeordered correlator). We expect these features to be universal properties of largeN quantum mechanics systems with emergent reparametrization symmetry. This article is largely based on talks given by Kitaev, which motivated us to work out the details of the ideas described there.
 Publication:

Physical Review D
 Pub Date:
 November 2016
 DOI:
 10.1103/PhysRevD.94.106002
 arXiv:
 arXiv:1604.07818
 Bibcode:
 2016PhRvD..94j6002M
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 58 pages plus appendices