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We investigate geometric phase (GP) of a qubit symmetrically coupled to a XYspin chain with three-spin interaction in a transverse magnetic field. Ananalytical expression for the GP is found in the weak coupling limit. It isshown that the GP displays a sharp peak or dip around the quantum phasetransition (QPT) point of the spin chain. Without the three-spin interaction,the GP has a peak or dip around the critical point $\lambda=1$. If thethree-spin interaction exists, the peak or dip position is obviously shiftedaway from the original position. This result reveals that the GP may be takenas an observable to detect both the existence and strength of multi-spininteraction in a spin chain.

Detecting multi-spin interaction of an XY spin chain by geometric phase of a coupled qubit