High-frequency transport and zero-sound in an array of SYK quantum dots

TL;DR

This paper investigates transport properties and zero-sound modes in an array of complex SYK quantum dots with added quadratic terms, revealing non-universal conductivities and collective excitations in a non-Fermi-liquid regime.

Contribution

It introduces a theoretical framework for analyzing transport and collective modes in SYK arrays with quadratic perturbations, extending understanding of non-Fermi-liquid behavior.

Findings

Non-universal, temperature-dependent Lorenz ratio at low frequencies.

Presence of zero-sound-like collective mode with nearly linear dispersion.

Insights into the origin of heavy Fermi liquids with large Kadowaki-Woods ratio.

Abstract

We study an array of strongly correlated quantum dots of complex SYK type and account for the effects of quadratic terms added to the SYK Hamiltonian; both local terms and inter-dot tunneling are considered in the non-Fermi-liquid temperature range $T \gg T_{FL}$. We take into account soft-mode fluctuations and demonstrate their relevance for physical observables. Electric $\sigma(\omega,p)$ and thermal $\kappa(\omega,p)$ conductivities are calculated as functions of frequency and momentum for arbitrary values of the particle-hole asymmetry parameter $\mathcal{E}$. At low-frequencies $\omega \ll T$ we find the Lorenz ratio $L = \kappa(0,0)/T\sigma(0,0)$ to be non-universal and temperature-dependent. At $\omega \gg T$ the conductivity $\sigma(\omega,p)$ contains a pole with nearly linear dispersion $\omega \approx sp\sqrt{\ln\frac{\omega}{T}}$ reminiscent of the "zero-sound", known for Fermi-liquids. We demonstrate also that the developed approach makes it possible to understand the origin of heavy Fermi liquids with anomalously large Kadowaki-Woods ratio.