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

Path-integral Monte Carlo for the Gauge-fixed Berry Connection and the Local Z_2 Berry Phase