Quantum Fluctuations of the Dipole Moment of Electronic Systems as Conductivity Probes; Quantitative Ground State Computations in the Hubbard Model

We accurately compute correlation functions involving the dipole moment of the electrons in the Hubbard model to study fermion localization in quantum many-body systems, as suggested in Phys. Rev. Lett. 82, 370 (1999) and Eur. Phys. J. B 79, 121 (2011). Leveraging the exact solution in the one-dimensional case, we assess our ability to use such correlation functions as probes for conductivity. In particular, we address the minimum value of the gap that can lead to the proper classification of a system as an insulator by numerically studying finite systems through correlated methodologies such as Quantum Monte Carlo. We discuss the technical difficulties, including the shell effects and potential limitations in higher dimensional models.