Geometric phases and entanglement of two qubits with XY type interaction

K. Berrada, S. Abdel‐Khalek, C. H. Raymond Ooi

Xiu-Xing Zhang, Aiping Zhang, Fuli Li

J.E. Avron, O. Kenneth

Li Zhi-Jian, Xinlu Cheng, Wen Jiao-Jin

We consider a two-qubit system described by the Heisenberg XY model with Dzyaloshinski–Moriya (DM) anisotropic interaction in a perpendicular magnetic field to investigate the relation between entanglement, geometric phase and quantum phase transition (QPT). It is shown that the DM interaction has an effect on the critical boundary. The combination of entanglement and geometric phase may characterize QPT completely. Their jumps mean that the occurrence of QPT and inversely the QPT at the critical point at least corresponds to a jump of one of them.

Erik Sjöqvist

Aiping Zhang, Fuli Li

We consider a qubit symmetrically and transversely coupled to an XY spin chain with Dzyaloshinsky—Moriya (DM) interaction in the presence of a transverse magnetic field. An analytical expression for the geometric phase of the qubit is obtained in the weak coupling limit. We find that the modification of the geometrical phase induced by the spin chain environment is greatly enhanced by DM interaction in the weak coupling limit around the quantum phase transition point of the spin chain.