$\mathit{\text{Ab}}\mathit{\text{initio}}$ $\mathit{\text{GW}}$-BSE theory of optical activity in $\alpha$-quartz

We present an ab initio many-body theory of optical activity in solids within the GW-BSE framework. Dielectric spatial dispersion is formulated in two complementary forms: exciton envelope modulation and sum-over-exciton-states expansion. Our application to $\alpha$-quartz reveals that the envelope-modulated formulation captures the low-frequency region, whereas the sum-over-exciton-states formulation is essential to reproduce the correct full frequency dependence. Comparisons with the independent-particle approximation and simple local-field corrections further highlight the decisive role of excitonic many-body effects in shaping the spectral dispersion of optical activity in solids.