Dispersive SYK model: band structure and quantum chaos

TL;DR

This paper introduces a dispersive SYK model with hopping in 1+1 dimensions, exploring its band structure, quantum chaos, and crossover from dispersive to incoherent metal states, revealing effects of Van Hove singularities and topology.

Contribution

It extends the SYK model to higher dimensions with hopping, analyzing the resulting band structure, chaos, and metal-insulator crossover phenomena.

Findings

Crossover from dispersive to incoherent metal with changing temperature or hopping strength

Lyapunov exponent increases near Van Hove singularities due to high density of states

Topological band effects are discussed in the context of the model

Abstract

The Sachdev-Ye-Kitaev (SYK) model is a concrete model for non-Fermi Liquid with maximally chaotic behavior in $0+1$-$d$. In order to gain some insights into real materials in higher dimensions where fermions could hop between different sites, here we consider coupling a SYK lattice by a constant hopping. We call this dispersive SYK model. Focusing on $1+1$-$d$ homogeneous hopping, by either tuning temperature or the relative strength of random interaction (hopping) and constant hopping, we find a crossover between a dispersive metal to an incoherent metal, where dynamic exponent $z$ changes from $1$ to $\infty$. We study the crossover by calculating spectral function, charge density correlator and the Lyapunov exponent. We further find the Lyapunov exponent becomes larger when the chemical potential is tuned to approach a Van Hove singularity because of the large density of states near the Fermi suface. The effect of the topological non-trivial bands is also discussed.