Geometric Phase for a Qutrit-Qubit Mixed-Spin System

We study the geometric phase of a qutrit-qubit mixed-spin system in an external homogeneous magnetic field. Both the spin-spin interaction strength J and the external magnetic field B can affect the geometric phase of the system. In addition, we consider the negativity of the composite system. The relationship between the negativity and the geometric phase is obtained. Finally, we calculate the geometric phase for a thermal mixed state and show how the geometric phase depends on the rescaled coupling parameter and temperature. In the limit T→0, we can recover the result of the ground state. This analysis has some implications in realistic implementations of geometric quantum computation.