  Predicting the thermal conductivity of glasses from first principles has
hitherto been a prohibitively complex problem. In fact, past works have
highlighted challenges in achieving computational convergence with respect to
length and/or time scales using either the established Allen-Feldman or
Green-Kubo formulations, endorsing the concept that atomistic models containing
thousands of atoms -- thus beyond the capabilities of first-principles
calculations -- are needed to describe the thermal conductivity of glasses. In
addition, these established formulations either neglect anharmonicity
(Allen-Feldman) or miss the Bose-Einstein statistics of atomic vibrations
(Green Kubo), thus leaving open the question on the relevance of these effects.
Here, we present a first-principles formulation to address the thermal
conductivity of glasses above the plateau, which can account comprehensively
for the effects of structural disorder, anharmonicity, and quantum
Bose-Einstein statistics. The protocol combines the Wigner formulation of
thermal transport with convergence-acceleration techniques, and is validated in
vitreous silica using both first-principles calculations and a quantum-accurate
machine-learned interatomic potential. We show that models of vitreous silica
containing less than 200 atoms can already reproduce the thermal conductivity
in the macroscopic limit and that anharmonicity negligibly affects heat
transport in vitreous silica. We discuss the microscopic quantities that
determine the trend of the conductivity at high temperature, highlighting the
agreement of the calculations with experiments in the temperature range above
the plateau where radiative effects remain negligible (50<T <450 K).
