Ground State Quantum Fluctuations of Electric Dipole Moment as Probes for Electrical Conductivity*

Electrical conductivity is a fundamental property of a material that measures its ability to respond to an electric field. While we are familiar with some materials being insulators and some being metals, from the theoretical point of view, it may be very challenging to detect a metal-insulator transition starting from the microscopic Hamiltonian. The difficulty lies in the fact that conductivity is a dynamical response function, and it is mainly governed by the excited states of the Hamiltonian itself, making its calculations computationally expensive and theoretically formidable. Focusing on the celebrated Fermi-Hubbard Hamiltonian, we study and assess the quantum fluctuations of the electric dipole moment of the system as a computational probe that can distinguish between a metal and an insulator just relying on the ground state physics.