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

TL;DR

This paper investigates thermal transport and quantum chaos in a large-N anharmonic lattice model, revealing a quantum phonon fluid regime with Planckian timescales and the impact of acoustic phonons and Goldstone modes on diffusivities.

Contribution

It introduces a large-N lattice model with anharmonic interactions, analyzing the interplay of optical and acoustic phonons on transport and chaos, highlighting the role of Goldstone modes in strongly coupled systems.

Findings

Thermal and chaos diffusivities are proportional with a factor near 1.

In the quantum phonon fluid regime, diffusivities scale inversely with temperature.

Long-wavelength acoustic phonons remain long-lived due to Goldstone's theorem.

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 $D_{\rm th}$ 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 $D_{\rm th} \approx \gamma D_L$ 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 $\hbar/k_B T$. 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 $D_{\rm th}/D_L\to \infty$, while for $d=3$, $D_{\rm th}$ and $D_{L}$ remain comparable.