  We study the ground-state properties of the S=1/2 antiferromagnetic
Heisenberg model on the Union Jack strip lattice by using the
exact-diagonalization and density matrix renormalization group methods. We
confirm a region of the intermediate-magnetization state between the Neel-like
spin liquid state and the conventional ferrimagnetic state of Lieb-Mattis type.
In the intermediate-state, we find that the spontaneous magnetization changes
gradually with respect to the strength of the inner interaction. In addition,
the local magnetization clearly shows an incommensurate modulation with
long-distance periodicity in the intermediate-magnetization state. These
characteristic behaviors lead to the conclusion that the
intermediate-magnetization state is the non-Lieb-Mattis ferrimagnetic one. We
also discuss the relationship between the ground-state properties of the S=1/2
antiferromagnetic Heisenberg model on the original Union Jack lattice and those
on our strip lattice.
