Correlated quantum shift vector diagnoses localization of particle-hole excitations

Electron interactions play a critical role in optical response. A prime example is excitonic transitions with energies that peel away from the single particle-hole continuum. We demonstrate that, beyond spectral properties, strong electron-hole interactions produce a correlated excitonic quantum geometry with optical properties distinct from weakly interacting particle-hole excitations. Strikingly, we find excitonic shift vectors are insensitive to light polarization; vertical excitonic transitions produce vanishing shift vectors in non-polar space groups zeroing excitonic shift photocurrents. These features are not shared by weakly interacting delocalized interband transitions rendering the quantum shift vector a sharp optical diagnostic of the bound nature of photoexcitation. This provides an instructive non-perturbative example of how interactions radically transform excited state quantum geometry.