Quantum entanglement in low dimensional spin systems

This thesis is composed of two parts in which quantum entanglement is investigated in the low dimensional spin systems. In the first part, we have numerically calculated the thermal entanglement of a two qubit system at low temperatures in an isotropic Ising chain under an inhomogeneous magnetic field. It is shown that in the inhomogeneous magnetic field, the two qubit system has entangled states. It is concluded that the presence of the inhomogeneity in the magnetic field plays an effective role on the entangled states.In the second part, we investigate thermal entanglement of a two qutrit Ising chain in the presence of an external magnetic field and Dzialoshinski-Moriya (DM) interaction. Influences of magnetic field, temperature, and DM interaction on the entanglement have been characterized in terms of negativity. The cases of parallel, antiparallel, and transverse magnetic fields are considered. Results of detailed numerical calculations are explained using the analytically determined ground and excited states of the system. Finally, we show that at a given temperature, control of entanglement can be optimized by utilizing competing effects of the magnetic field and the DM interaction.