  We present a general formula of the gauge-fixed Berry connection which can be
evaluated by path- integral Monte Carlo method. We also propose that the
gauge-fixed local Berry connection can be an- other effective tool to estimate
precisely the quantum critical point. For a demonstration, we calculate the
gauge-fixed Berry connection and the local Z2 Berry phase of the
antiferromagnetic Heisenberg model on a staggered bond-alternating ladder, and
estimated quantum critical point is consistent with other methods.
