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

We study properties of thermal transport and quantum many-body chaos in a lattice model with N→∞ oscillators per site, coupled by strong anharmonic terms. We first consider a model with only optical phonons. We find that the thermal diffusivity Dth and chaos diffusivity DL (defined as DL=vB2/λL, where vB and λL are the butterfly velocity and the scrambling rate, respectively) satisfy Dth≈γDL with γ1. At intermediate temperatures, the model exhibits a quantum "phonon fluid"regime, where both diffusivities satisfy D-1T, and the thermal relaxation time and inverse scrambling rate are of the order the of Planckian timescale /kBT. 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 Dth/DL→∞, while for d=3, Dth and DL remain comparable.