Correlated quantum shift vector of particle-hole excitations

Excitons are a prime example of how electron interactions affect optical response and excitation. For example, electron-hole interactions produce a bound excitonic spectrum. Here we show that, beyond its spectra, the bound nature of an exciton's electron-hole pair produces a correlated quantum geometry: excitonic excitations possess a quantum shift vector that is independent of light polarization. We find this counterintuitive behavior has dramatic consequences for geometric response: e.g., in noncentrosymmetric but non-polar materials, vertical excitonic transitions possess vanishing shift vector zeroing their shift photocurrent; this contrasts with finite and strongly light polarization dependent shift vectors for non-interacting delocalized particle-hole excitations. This dichotomy makes shift vector a sharp diagnostic of the pair localization properties of particle-hole excitations and demonstrates the non-perturbative effects of electron interactions in excited state quantum geometric response.