Critical entanglement and geometric phase of a two-qubitmodel with Dzyaloshinski--Moriya anisotropic interaction

We consider a two-qubit system described by the HeisenbergXY model with Dzyaloshinski--Moriya (DM) anisotropic interactionin a perpendicular magnetic field to investigate the relationbetween entanglement, geometric phase and quantum phase transition(QPT). It is shown that the DM interaction has an effect on thecritical boundary. The combination of entanglement and geometricphase may characterize QPT completely. Their jumps mean that the occurrenceof QPT and inversely the QPT at the critical point at leastcorresponds to a jump of one of them.