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

Aleksey. V. Lunkin, Mikhail . V. Feigel'man

SciPost Phys. 13, 073 (2022) · published 29 September 2022

- doi: 10.21468/SciPostPhys.13.3.073
- Submissions/Reports

### 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.

### Cited by 2

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}^{2}Lunkin Aleksey, -
^{2}Mikhail V. Feigel'man

^{1}Высшая школа экономики / National Research University Higher School of Economics [HSE]^{2}Институт теоретической физики им. Л. Д. Ландау / Landau Institute for Theoretical Physics