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}T≫TFL. We take into account soft-mode fluctuations and demonstrate their relevance for physical observables. Electric \sigma(\omega,p)σ(ω,p) and thermal \kappa(\omega,p)κ(ω,p) conductivities are calculated as functions of frequency and momentum for arbitrary values of the particle-hole asymmetry parameter \mathcal{E}ℰ. At low-frequencies \omega \ll Tω≪T we find the Lorenz ratio L = \kappa(0,0)/T\sigma(0,0)L=κ(0,0)/Tσ(0,0) to be non-universal and temperature-dependent. At \omega \gg Tω≫T the conductivity \sigma(\omega,p)σ(ω,p) contains a pole with nearly linear dispersion \omega \approx sp\sqrt{\ln\frac{\omega}{T}}ω≈splnωT 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.

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