  In this paper, we determine the geometric phase for the one-dimensional $XXZ$
Heisenberg chain with spin-$1/2$, the exchange couple $J$ and the spin
anisotropy parameter $\Delta$ in a longitudinal field(LF) with the reduced
field strength $h$. Using the Jordan-Wigner transformation and the mean-field
theory based on the Wick's theorem, a semi-analytical theory has been developed
in terms of order parameters which satisfy the self-consistent equations. The
values of the order parameters are numerically computed using the
matrix-product-state(MPS) method. The validity of the mean-filed theory could
be checked through the comparison between the self-consistent solutions and the
numerical results. Finally, we draw the the topological phase diagrams in the
case $J<0$ and the case $J>0$.
