Seeking to develop global SYK-ness

TL;DR

This paper explores a class of multi-flavored fermion systems aiming to realize a spatially-dispersing 'globally-SYK' phase, extending the SYK model beyond local interactions to include nonlocal, algebraically decaying interactions.

Contribution

It introduces a framework for achieving globally dispersing SYK behavior through nonlocal interactions, contrasting with traditional local SYK models.

Findings

Identification of conditions for globally dispersing SYK behavior

Analysis of thermodynamic properties of nonlocal SYK systems

Discussion of transport properties in spatially-dispersing SYK models

Abstract

Inspired by the recent interest in the Sachdev-Ye-Kitaev (SYK) model we study a class of multi-flavored one- and two-band fermion systems with no bare dispersion. In contrast to the previous work on the SYK model that would routinely assume spatial locality, thus unequivocally arriving at the so-called 'locally-critical' scenario, we seek to attain a spatially-dispersing 'globally-SYK' behavior. To that end, a variety of the Lorentz-(non)invariant space-and/or-time dependent algebraically decaying interaction functions is considered and some of the thermodynamic and transport properties of such systems are discussed.