The photoluminescence spectrum of a single-layer boron nitride remains elusive, marked by enigmatic satellites that hint at significant but unidentified exciton-phonon coupling. Here, by employing a first-principles approach based on the many-body cumulant expansion of the charge response, we calculate the optical absorption and photoluminescence of a single-layer boron nitride. We identify the specific exciton-phonon scattering channels and unravel their impact on the optical absorption and photoluminescence spectra, thereby providing an interpretation of the experimental features. Finally, we show that, even in a strongly polar material such as h-BN monolayer, the electron-hole interaction responsible for the excitonic effect results in the cancellation of the Frölich interaction at small phonon momenta. This effect is captured only if the invariance of the exciton-phonon matrix elements under unitary transformations in the Bloch function manifold is preserved in the calculation.
Keywords: 2D materials; absorption; cumulant approach; first-principles calculations; photoluminescence.