nt - p h / 06 02 08 9 v 1 10 F eb 2 00 6 Relation between concurrence and Berry phase of an entangled state of two spin 1 / 2 particles

In the last few years Berry phase in a single particle system has been studied very well, both theoretically and experimentally. However, the study of Berry phase in an entangled state has become a topic of interest very recently [1, 2, 3, 4, 5]. As entanglement is a striking feature of quantum systems and is a useful resource to realize quantum information, quantum teleportation, quantum cryptography or quantum computation, the study of entangled state has absorbed much attention. We have to be careful about two aspects of Berry phase of an entangled state. One is how it changes due to interparticle interaction [1, 2, 3] and the other is how it affects [4] the biparticle states. The motivation of this letter is to see the effect of the Berry phase on an entangled system of two spin-1/2 particles. As a result we have also found a connection between it and the concurrence (which is the measure of of entanglement) for different spin chains. It is well known that a fermion which is a spin 1/2 particle can be realized when a scalar particle is attached with a magnetic flux quantum. The attachment of the magnetic flux quantum changes the spin and statistics of the scalar particle. The effect of the flux quantum is to induce an appropriate AharanovBohm phase which simulates the statistical phase factor. For one complete rotation the wave function of a fermion acquires an extra geometric phase known as Berry phase besides the dynamical phase. The attachment of magnetic flux quantum to a scalar particle is also equivalent to the motion of a charged particle in the field of a magnetic monopole of strength 2b where b is a half integer or integer. The angular momentum of the particle can be written as