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 time scale $\hslash /k_{B}T$.

Typos corrected, references added, discussion improved

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• Classical and quantum butterfly effect in nonlinear vector mechanics
• Thermal diffusivity and its lower bound in orthorhombic SnSe
• A Sport and a Pastime: Model Design and Computation in Quantum Many-Body Systems
• Defect conformal field theory from Sachdev-Ye-Kitaev interactions
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• The quantum $p$-spin glass model: A user manual for holographers
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• Can electronic quantum criticality drive phonon-induced linear-in-temperature resistivity?