Geometric phase of a central qubit coupled to a spin chain in a thermal equilibrium state

► To extend the geometric phase (GP) approach to finite temperature. ► To consider a central qubit weakly coupled to a XY spin chain in a thermal equilibrium state. ► An explicit analytical expression of the GP for the coupled qubit is obtained. ► The variation of the GP of the coupled qubit can well indicate the signature of QPT in a finite range of temperature. ► The GP can be used as a theoretical indicator of a phase transition.