As a measure to ascertain whether a system is metallic or insulating, localization length $lambda_N$, which represents the spread of electron distribution, can be a useful quantity, especially for approaching a metal-insulator transition from the ins
ulator side. We try to calculate $lambda_N$ using a variational Monte Carlo method for normal (paramagnetic), superconducting and antiferromagnetic states in the square-lattice Hubbard model. It is found that the behavior of $lambda_N$ is consistent with what is expected from other quantities, and gives information complementary to another measure, the Drude weight.
