Investigation of quantum entanglement in mixed type Heisenberg spin systems

In recent years, entanglement appears at the center of quantum computation and quantum information studies which emerged as an interdisciplinary field. Entanglement can be realized in Heisenberg spin systems and its change is investigated with respect to various control parameters such as magnetic field, anisotropy parameter and DM interaction in the system. Heisenberg spin systems are used to investigate the structure of the physical systems in the study of condensed matter physics. It seems highly probable that in near future the knowledge of quantum and condensed matter physics will be used in the technological applications of the entanglement producing systems. Therefore, in this study, entanglement of different mixed-type Heisenberg XXX spin systems in a homogeneous magnetic field is investigated. The ground state and thermal entanglement of these systems are calculated by using the negativity under the periodic boundary conditions. In the first part of the thesis, the ground state and thermal entanglement of two spins mixed-type Heisenberg XXX spin systems are investigated. We have found that spin (1, 3/2) mixed spin system is more entangled than spin (1/2, 1) and spin (1/2, 3/2) mixed spin systems and both the critical temperature and the critical magnetic field values for spin (1, 3/2) are greater than spin (1/2, 1) and spin (1/2, 3/2) systems. In the second part, ground state and thermal entanglement in Heisenberg XXX system which is designed as mixed spin (1/2, 1, 3/2), is studied in both cases in the presence of the nearest neighboring (NN) interaction and in the presence of both NN and the next nearest neighboring (NNN) interactions. The entanglement in spin (1, 3/2) subsystem is greater than the spin (1/2, 1) and spin (1/2, 3/2) subsystems. It is also found that the presence of the third spin in this designed system generally reduces the entanglement. Also, the presence of NNN interactions increases the strength of the entanglement against the magnetic field.