Higher Dimensional Generalizations of the SYK Model

TL;DR

This paper introduces a 1+1 dimensional generalization of the SYK model with lattice structure, revealing new IR scaling behaviors and interactions, bridging SYK physics with field theory and external probes.

Contribution

It presents a novel 1+1D lattice SYK model with momentum-restricted interactions and explores diverse IR hyperscaling phenomena and external fermion probing.

Findings

Discovery of a class of low-pass filters leading to varied hyperscaling in IR

Identification of new IR scaling behaviors with external fermion probes

Connection between lattice SYK models and field theory regimes

Abstract

We discuss a 1+1 dimensional generalization of the Sachdev-Ye-Kitaev model. The model contains $N$ Majorana fermions at each lattice site with a nearest-neighbour hopping term. The SYK random interaction is restricted to low momentum fermions of definite chirality within each lattice site. This gives rise to an ordinary 1+1 field theory above some energy scale and a low energy SYK-like behavior. We exhibit a class of low-pass filters which give rise to a rich variety of hyperscaling behaviour in the IR. We also discuss another set of generalizations which describes probing an SYK system with an external fermion, together with the new scaling behavior they exhibit in the IR.