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 inter-dot tunneling are considered in the non-Fermi-liquid temperature range T≫TFL. We take into account soft-mode fluctuations and demonstrate their relevance for physical observables. Electric σ(ω,p) and thermal κ(ω,p) conductivities are calculated as functions of frequency and momentum for arbitrary values of the particle-hole asymmetry parameter E. At low-frequencies ω≪T we find the Lorenz ratio L=κ(0,0)/Tσ(0,0) to be non-universal and temperature-dependent. At ω≫T the conductivity σ(ω,p) contains a pole with nearly linear dispersion ω≈sp√lnωT 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.
SciPost Phys. 12, 031 (2022) ·
published 20 January 2022
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We consider a non-equilibrium generalization of the mixed SYK4+SYK2 model and calculate the energy dissipation rate W(ω) that results due to periodic modulation of random quadratic matrix elements with a frequency ω. We find that W(ω) possesses a peak at ω close to the polaron energy splitting ωR 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 ωR and calculate, in presence of this pumping, non-equilibrium dissipation rate due to low-frequency parametric modulation. We found an unusual phenomenon similar to "dry friction" in presence of pumping.
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