Ground State Conductivity Probes in the One-Dimensional Hubbard Model

Using quantum Monte Carlo simulation, we compute quantum metric tensor and localization length in the ground state of the one-dimensional Fermi-Hubbard Hamiltonian, as probes for conductivity. We compare these values with the exact values of the charge gap of the system as a function of the interaction strength. We perform calculations for lattices with up to 1000 sites, at half-filling, using both periodic and open boundary conditions. We assess and discuss the sensitivity of the probes mentioned above in detecting a metal-insulator phase transition. We suggest data analysis methodologies to deal with the finite-size effects. We will also show preliminary results in two dimensions.