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

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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 interdot tunneling are considered in the nonFermiliquid temperature range $T \gg T_{FL}$. We take into account softmode 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 particlehole asymmetry parameter $\mathcal{E}$. At lowfrequencies $\omega \ll T$ we find the Lorenz ratio $L = \kappa(0,0)/T\sigma(0,0)$ to be nonuniversal and temperaturedependent. 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 "zerosound", known for Fermiliquids. We demonstrate also that the developed approach makes it possible to understand the origin of heavy Fermi liquids with anomalously large KadowakiWoods ratio.
SciPost Phys. 12, 031 (2022) ·
published 20 January 2022

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We consider a nonequilibrium generalization of the mixed SYK$_4$+SYK$_2$ model and calculate the energy dissipation rate $W(\omega)$ that results due to periodic modulation of random quadratic matrix elements with a frequency $\omega$. We find that $W(\omega)$ possesses a peak at $\omega$ close to the polaron energy splitting $\omega_R$ found recently (PRL 125, 196602), demonstrating the physical significance of this energy scale. Next, we study the effect of energy pumping with a finite amplitude at the resonance frequency $\omega_R$ and calculate, in presence of this pumping, nonequilibrium dissipation rate due to lowfrequency parametric modulation. We found an unusual phenomenon similar to "dry friction" in presence of pumping.