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

TL;DR

This paper demonstrates that the geometric phase of a coupled qubit can serve as an observable to detect and measure multi-spin interactions in an XY spin chain, especially near quantum phase transitions.

Contribution

It provides an analytical expression for the geometric phase in a coupled qubit-spin chain system and shows how it reveals multi-spin interactions through shifts in critical behavior.

Findings

GP exhibits sharp peaks or dips near QPT points

Presence of three-spin interaction shifts GP features away from standard critical points

GP can be used to detect and quantify multi-spin interactions

Abstract

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 (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 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.