A bipartite Sachdev-Ye-Kitaev model: Conformal limit and level statistics

TL;DR

This paper introduces a bipartite version of the SYK model, demonstrating its solvability, tunable scaling dimensions, and distinct spectral properties, including altered level statistics and an exchange symmetry.

Contribution

It presents a solvable bipartite SYK model with tunable dimensions and analyzes its spectral properties, revealing differences from the original model.

Findings

Model remains solvable at large N with finite flavor ratio

Scaling dimensions can be tuned continuously

Level statistics differ from the original SYK model

Abstract

We study a bipartite version of the Sachdev-Ye-Kitaev (SYK) model. We show that the model remains solvable in the limit of large-$N$ in the same sense as the original model if the ratio of both flavors is kept finite. The scaling dimensions of the two species can be tuned continuously as a function of the ratio. We also investigate the finite-size spectral properties of the model. We show how the level statistics differs from the original SYK model and infer an additional exchange symmetry in the bipartite model.