Thermal expansion mechanisms, heat transport, and band-gap renormalization in strongly anharmonic Rb$_2$SO$_4$, Rb$_2$Ca$_2$(SO$_4$)$_3$, and Ba$_3$Lu(BO$_3$)$_3$ from machine-learned interatomic potentials

Rb$_2$SO$_4$, Rb$_2$Ca$_2$(SO$_4$)$_3$, and Ba$_3$Lu(BO$_3$)$_3$ are structurally complex materials whose thermal expansion has been interpreted, on the basis of high-temperature x-ray diffraction, in terms of specific polyhedral rearrangements. We study their lattice dynamics and its consequences f