Strongly coupled quantum phonon fluid in a solvable model

Abstract

We study a model of a large number of strongly coupled phonons that can be viewed as a bosonic variant of the Sachdev-Ye-Kitaev model. We determine the phase diagram of the model which consists of a glass phase and a disordered phase, with a first-order phase transition separating them. We compute the specific heat of the disordered phase, with which we diagnose the high-temperature crossover to the classical limit. We further study the real-time dynamics of the disordered phase, where we identify three dynamical regimes as a function of temperature. Low temperatures are associated with a semiclassical regime, where the phonons can be described as long-lived normal modes. High temperatures are associated with the classical limit of the model. For a large region in parameter space, we identify an intermediate-temperatures regime, where the phonon lifetime is of the order of the Planckian timescaleh/k B T .

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

“…In this section, we highlight the main properties of the zero-dimensional (0D) model we studied in [43]. This model serves as a single unit cell of the lattice model we consider in this work.…”

“…The relaxation time was found to obey τ th = ατ Pl , with α ≈1-3, in opposed to good thermal conductors such as diamond, where the same procedure yields α ∼ 50 [41]. The appearance of the Planckian timescale at these elevated temperatures is particularly counter-intuitive as one would naively expect the dynamics to be essentially classical, with α 1 [43]. In addition, the observation of such short transport times has the interesting implication that these materials might be described in terms of a strongly coupled "phonon fluid", similarly to the "soup" in [38].…”

“…These exciting observations motivated us to formulate a theoretical framework where thermal transport and many-body quantum chaos can be systematically studied in a model of strongly coupled phonons. In our previous work [43], we considered a zero-dimensional model of strongly coupled nonlinear oscillators. We demonstrated that the real-time dynamics, probed by the phonon lifetime, exhibits a "phonon fluid" regime at intermediate temperatures, where the phonon lifetime is of the order of the Planckian timescale.…”

“…1 for a schematic summary. In this work, we study properties of thermal transport and quantum many-body chaos in a lattice generalization of [43]. This paper is organized as follows.…”

“…In Sec. III, we discuss a lattice generalization of [43] and summarize our main results on transport and chaos. In Sec.…”