A320 Captain reported an inadvertent release of the aircraft parking brake after arriving at the gate; resulting in unwanted aircraft movement.

Narrative

A single engine taxi was being completed after landing and taxiing to gate X in ZZZ.. A marshaller and two wing walkers were confirmed prior to proceeding on the lead in line. I noted the fact the jetway at this gate is fixed and a precise stop is required for successful parking and attaching the jetway. I was moving very slowly and was given the stop signal from the marshaller. At this time; I set the parking brake and verbally and by pointing confirmed the parking brake message was displayed; the triple gauge showed brake pressure on both brakes and accumulator pressure in the green. I then directed the First Officer to shut down the number one engine. As the aircraft power switched to APU generator; the parking brake seemed to release and the aircraft moved forward approximately five feet. I immediately sensed the motion and applied manual toe brakes to stop the aircraft. The marshaller also saw the movement and got in to a position to get my attention that the aircraft was moving. After confirming we were chocked; I released the toe brakes and cycled the parking brake handle. A tug was then attached; to push the aircraft back to the proper position. A maintenance write up was entered and local maintenance notified. We completed a verbal brief with the maintenance technician.