  Employing extensive cellular dynamical mean-field theory (CDMFT) calculations
with exact diagonalization impurity solver, we investigate the ground state
phase diagrams and non-magnetic metal-insulator transitions of the half-filled
Hubbard model on two plaquette -- the 1/5 depleted and checkerboard -- square
lattices. We identify three different insulators in the phase diagrams: dimer
insulator, antiferromagnetic insulator, and plaquette insulator. And we
demonstrate that the plaquette insulator is a novel fragile Mott insulator
(FMI) which features a nontrivial one-dimensional irreducible representation of
the $C_{4v}$ crystalline point-group and cannot be adiabatically connected to
any band insulator with time-reversal symmetry. Furthermore, we study the
non-magnetic quantum phase transitions from the metal to the FMI and find that
this Mott metal-insulator transition is characterized by the splitting of the
non-interacting bands due to interaction effects.
