Sachdev-Ye-Kitaev model as Liouville quantum mechanics

We show that the proper inclusion of soft reparameterization modes in the Sachdev-Ye-Kitaev model of N randomly interacting Majorana fermions reduces its long-time behavior to that of Liouville quantum mechanics. As a result, all zero temperature correlation functions decay with the universal exponent alpha tau(-3/2) for times larger than the inverse single particle level spacing tau >> N ln N. In the particular case of the single particle Green function this behavior is manifestation of the zero-bias anomaly, or scaling in energy as is an element of(1/2). We also present exact diagonalization study supporting our conclusions. (C) 2016 The Author(s). Published by Elsevier B.V.