Geometrical Probes for Conductivity in the Hubbard Model

We explore the possibility of studying the conductivity of a quantum many-body system entirely relying on the ground-state wave function of the system itself. While, in general, we would need access to the entire manifold of the excited states of a system to compute the conductivity tensor, ground states estimators have been proposed to decide whether a system is conducting or insulating. Using the Hubbard Model as an example, we run quantum Monte Carlo calculations to assess the accuracy and reliability of such probes. In addition, we use exact diagonalization to discuss the physical meaning of such estimators.