Excitons in Large Disordered Boron-Nitride Layer using Linear-Scaling Bethe-Salpeter Simulations

We introduce a real-space, linear-scaling Bethe-Salpeter framework that enables excitonic spectroscopy in large and possibly disordered boron-nitride-derived systems. Thanks to the use of a sublattice-resolved perturbative decoupling that maps localized electron-hole pairs onto a sparse tight-binding model, we implement the Kernel Polynomial Method to compute absorption spectra with O(N) cost. To illustrate the capabilities of our method, we apply it to Anderson-disordered monolayer hexagonal boron nitride with up to $10^{5}$ orbitals. The method reveals a disorder-induced asymmetric broadening of bright excitons, a crossover from quadratic to linear redshift of the main absorption peak, and Anderson localization of the exciton center of mass. This approach extends excitonic calculations beyond the reach of conventional ab initio Green's function methods (GW approximation and Bethe-Salpeter equation), opening optical spectroscopy to large-scale, disordered, moir\'e, quasicrystalline, and structurally complex quantum materials.