Not yet reviewed by Pith; the record is open.

Monolayer hexagonal boron nitride is a prototypical planar 2-dimensional system material and has been the subject of many investigations of its exceptional vibrational, spectroscopic and transport properties. The lattice thermal conductivity remains quite uncertain, with theoretical and experimental reports varying between 218 and 1060 Wm-1K-1. It has a strong temperature evolution and is sensitive to strain effects and isotope concentrations. While the impact of isotope scattering has been widely studied and is well understood, nuclear quantum effects and 4-phonon scattering have so far been neglected. Monolayer hexagonal boron nitride is composed of light elements, and further has its 3-phonon scattering phase space restricted by mirror plane symmetry, so these effects may be of similar order as isotope scattering, and would lead to a completely different understanding of the fundamental processes limiting the lattice thermal conductivity for this system. In this work, we use both classical and path-integral molecular dynamics, in conjunction with the Temperature Dependent Effective Potential method, to compute temperature-dependent renormalized phonons including isotope scattering, 3-phonon scattering, 4-phonon scattering and nuclear quantum effects. We show the impact of the latter two on the lattice thermal conductivity for a large temperature range, as well as their impact on the phonon lifetimes. Overall, our work provides a robust framework for calculations of the lattice thermal conductivity in solids, providing quantitative improvements and physical understanding that help explain the variety of results found in the literature.