  On the basis of quantum Monte Carlo (QMC) simulations we study the formation
of Mott domains in the one-dimensional Hubbard model with an additional
confining potential. We find evidences of quantum critical behavior at the
boundaries of the Mott-insulating regions. A local compressibility defined to
characterize the local phases exhibits a non-trivial critical exponent on
entering the Mott-insulating domains. Both the local compressibility and the
variance of the local density show universality with respect to the confining
potential. We also study the momentum distribution function of the trapped
system, and determine its phase diagram.
