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

We investigate geometric phase (GP) of a qubit symmetrically coupled to a XY spin chain with three-spin interaction in a transverse magnetic field. An analytical expression for the GP is found in the weak coupling limit. It is shown that the GP displays a sharp peak or dip around the quantum phase transition point of the spin chain. Without the three-spin interaction, the GP has a peak or dip around the critical point λ=1. If the three-spin interaction exists, the peak or dip position is obviously shifted away from the original position. This result reveals that the GP may be taken as an observable to detect both the existence and strength of multi-spin interaction in a spin chain. -- Highlights: ► Analytical expression for geometric phase (GP) of a qubit coupled to a spin chain is obtained. ► Relation between GP and multi-spin interaction is investigated. ► Detection of multi-spin interaction by means of GP is proposed.