Computation of thermal conductivity based on Path Integral Monte Carlo methods

TL;DR

This paper introduces a quantum Monte Carlo approach using Path Integral Monte Carlo and Green-Kubo theory to accurately compute thermal conductivity in insulating solids at low temperatures, capturing quantum effects beyond classical methods.

Contribution

The work presents a novel quantum methodology combining PIMC and Green-Kubo theory to calculate thermal conductivity, accounting for quantum effects in phonon transport.

Findings

Quantum effects significantly influence low-temperature thermal conductivity.

Standard phonon-based models cannot explain the observed increase in conductivity.

A new transport lifetime parameter is identified from heat-current correlations.

Abstract

The calculation of thermal conductivity in insulating solids at temperatures below the Debye temperature is problematic, due to the breakdown of classical and semi-classical approaches. In this work, we present a fully 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 crystalline argon modeled by a Lennard-Jones potential, a paradigmatic system 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 at low temperatures cannot be explained within a standard Peierls-Boltzmann framework or quasi-harmonic approximation using phonon lifetimes alone. Instead, a distinct transport lifetime emerges from the analysis of heat-current correlations. Our results demonstrate that quantum Monte Carlo methods provide a robust, non-perturbative framework to investigate heat transport in insulating solids, beyond the limits of classical molecular dynamics and quasi-harmonic approximations.