Strongly coupled phonon fluid and Goldstone modes in an anharmonic quantum solid: transport and chaos

Abstract

We study properties of thermal transport and quantum many-body chaos in a lattice model with $N\to \infty$ oscillators per site, coupled by strong anharmonic terms. We first consider a model with only optical phonons. We find that the thermal diffusivity $D_{\mathrm{th}}$ and chaos diffusivity $D_L$ (defined as $D_L=v_B^2/{\lambda }_L$, where $v_B$ and ${\lambda }_L$ are the butterfly velocity and the scrambling rate, respectively) satisfy $D_{\mathrm{th}}\approx \gamma D_L$ with $\gamma \gtrsim 1$. At intermediate temperatures, the model exhibits a "quantum phonon fluid" regime, where both diffusivities satisfy $D^{-1}\propto T$, and the thermal relaxation time and inverse scrambling rate are of the order the of Planckian timescale $\hslash /k_{B}T$. We then introduce acoustic phonons to the model and study their effect on transport and chaos. The long-wavelength acoustic modes remain long-lived even when the system is strongly coupled, due to Goldstone's theorem. As a result, for $d=1,2$, we find that $D_{\mathrm{th}}/D_L\to \infty$, while for $d=3$, $D_{\mathrm{th}}$ and $D_L$ remain comparable.

16 + 9 pages, 8 + 1 figures, updated version to match published version

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