Quantifying entanglement in the one-dimensional Heisenberg spin chain

Abstract

This thesis aims to investigate the entanglement properties of the one-dimensional Heisenberg spin chain, with a focus on the entanglement between pairs of spins. Specifically, we explore how entanglement depends on temperature and coupling constants without an external magnetic field and then consider the effect of an external magnetic field on entanglement. To model the system, we utilize the Hamiltonian of the 1D Heisenberg spin chain and calculate the density matrix. We use the concurrence as a measure of entanglement, which is applicable to mixed state densities. Our main findings demonstrate that the entanglement between pairs of spins in the Heisenberg spin chain increases as temperature decreases or coupling constants increase. We also identify a critical range of magnetic fields in which the entanglement between spin pairs undergoes significant changes. Finally, we examine the relationship between entanglement and the number of lattice sites separating given pairs of spins. Our results reveal that as the number of lattice sites between pairs of spins increases, the entanglement between them decreases. Overall, this study provides insights into the entanglement properties of the one-dimensional Heisenberg spin chain and sheds light on the factors that influence entanglement in quantum systems. These findings potentially have important implications for the design and development of quantum information processing devices.