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arXiv · 1904.02174

Transport and chaos in lattice Sachdev-Ye-Kitaev models

Haoyu Guo·Yingfei Gu·Subir Sachdev
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Abstract

We compute the transport and chaos properties of lattices of quantum Sachdev-Ye-Kitaev islands coupled by single fermion hopping, and with the islands coupled to a large number of local, low energy phonons. We find two distinct regimes of linear-in-temperature ($T$) resistivity, and describe the crossover between them. When the electron-phonon coupling is weak, we obtain the `incoherent metal' regime, where there is near-maximal chaos with front propagation at a butterfly velocity $v_B$, and the associated diffusivity $D_{\rm chaos} = v_B^2/(2 πT)$ closely tracks the energy diffusivity. On the other hand, when the electron-phonon coupling is strong, and the linear resistivity is largely due to near-elastic scattering of electrons off nearly free phonons, we find that the chaos is far from maximal and spreads diffusively. We also describe the crossovers to low $T$ regimes where the electronic quasiparticles are well defined.

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Haoyu Guo, Yingfei Gu, Subir Sachdev. 2019-07-06. Transport and chaos in lattice Sachdev-Ye-Kitaev models. https://doi.org/10.1103/physrevb.100.045140

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