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 .

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Derivation of the EME couplingWe derive the low-energy effective Kondo lattice model with EME term starting from an Anderson-type model coupled to phonons; the Kondo term was already derived in Ref. [28]. The key new insight is as follows: the effective Kondo-like coupling that is generated between the Pd-electrons and Cr local moments involves an inter-layer hybridization, t cp,ij between sites i and j. If this coupling were to be affected by the fluctuations associated with the corresponding out-of-plane bond, t cp,ij will be renormalized by the displacement, ϕ