  Vertical density matrix algorithm (VDMA), a tensor product state formulation
of the ``higher-dimensional'' density matrix renormalization group, is applied
to the spin 1/2 antiferromagnetic XXZ model on the checkerboard lattice. The
VDMA was, in the preceding study, applied to the transverse field Ising model
on the square lattice and the three-dimensional classical Ising model. In the
present paper, its implementation procedure is modified in order to apply the
VDMA to the XXZ model. Numerical accuracy of the VDMA is investigated for the
XXZ model on the square lattice, which shows that the method gives reliable
results for the ground state energy. In the frustrated region, VDMA results are
compared with a simple calculation based on a magnetically disordered state. It
is found that the weakly frustrated region is in the N\'{e}el ordered phase,
while in the strongly frustrated region the realized phase cannot be identified
clearly by the obtained results.
