Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics

TL;DR

This paper demonstrates that including soft reparameterization modes in the Sachdev-Ye-Kitaev model simplifies its long-time behavior to Liouville quantum mechanics, revealing universal decay patterns in correlation functions and supporting findings with exact diagonalization.

Contribution

It shows that the long-time dynamics of the SYK model can be described by Liouville quantum mechanics when soft modes are properly included, revealing universal decay exponents.

Findings

Zero temperature correlations decay as τ^{-3/2} for large τ.

Single particle Green function exhibits energy scaling as ε^{1/2}.

Exact diagonalization supports the theoretical predictions.

Abstract

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 $\propto \tau^{-3/2}$ for times larger than the inverse single particle level spacing $\tau\gg N\ln N$. In the particular case of the single particle Green function this behavior is manifestation of the zero-bias anomaly, or scaling in energy as $\epsilon^{1/2}$. We also present exact diagonalization study supporting our conclusions.