The calculation of thermal conductivity in insulating solids at temperatures below the Debye temperature is problematic, due to the breakdown of classical and semiclassical approaches. In this Letter, we present a fully nonperturbative quantum methodology to compute thermal conductivity based on path integral Monte Carlo (PIMC) simulations combined with the Green-Kubo linear response theory. The method is applied to rare gas solids modeled by a Lennard-Jones potential, paradigmatic systems where quantum effects strongly affect both thermodynamic and transport properties. From PIMC simulations, we obtain the temperature-dependent phonon frequencies, lifetimes, and specific heat. From the imaginary time correlations of the energy current, we extract the thermal transport coefficients based on a physically motivated prior. We show that the experimentally observed increase of the thermal conductivity of argon and neon at low temperatures cannot be explained within a Peierls-Boltzmann framework using phonon linewidths at equilibrium. In contrast, a distinct transport lifetime emerges from the analysis of heat-current correlations. Our results demonstrate that quantum Monte Carlo methods provide a robust, nonperturbative framework to investigate heat transport in insulating solids, beyond the limits of classical molecular dynamics without relying on perturbative or semiclassical approximations.

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• Lattice dynamics
• Phonons
• Thermal conductivity
• Thermal transport
• Crystalline systems
• Insulators
• First-principles calculations
• Path-integral Monte Carlo
• Path-integral methods