Maximally localized exciton Wannier functions for solids

We introduce a maximally localized Wannier function representation of Bloch excitons, two-particle correlated electron-hole excitations, in crystalline solids, where the excitons are maximally localized with respect to an average electron-hole coordinate in real space. As a proof-of-concept, we illustrate this representation in the case of low-energy spin-singlet and -triplet excitons in cubic lithium fluoride, computed using the ab initio Bethe-Salpeter equation approach. We visualize the resulting maximally localized exciton Wannier functions (MLXWFs) in real space, detail the convergence of the exciton Wannier spreads, and demonstrate how Wannier-Fourier interpolation can be leveraged to obtain exciton energies and states at arbitrary exciton crystal momenta in the Brillouin zone. We further introduce an approach to treat the long-range dipolar coupling between singlet MLXWFs and discuss it in depth. The MLXWF representation sheds light on the fundamental nature of excitons and paves the way toward Wannier-based post-processing of excitonic properties, enabling the construction of ab initio exciton tight-binding models, efficient interpolation of the exciton-phonon vertex, the computation of Berry curvature associated with exciton bands, and beyond.