Magnetic Entanglement in Spin-1/2 XX Chains

Abstract

In the study of entanglement in a spin chain, people often consider the nearest-neighbor spins. The motivation is the prevailing role of the short range interactions in creating quantum correlation between the 1st neighbor (1N) spins. Here, we address the same question between farther neighbor spins. We consider the one-dimensional (1D) spin-1/2 XY model in a magnetic field. Using the fermionization approach, we diagonalize the Hamiltonian of the system. Then, we provide the analytical results for entanglement between the 2nd, 3rd and 4th neighbor (denoted as 2N, 3N, and 4N respectively) spins. We find a magnetic entanglement that starts from a critical entangled-field ($h_c^E$) at zero temperature. The critical entangled-field depends on the distance between the spins. In addition to the analytical results, the mentioned phenomenon is confirmed by the numerical Lanczos calculations. By adding the temperature to the model, the magnetic entanglement remains stable up to a critical temperature, $T_c$. Our results show that entanglement spreads step by step to farther neighbors in the spin chain by reducing temperature. At first, the 1N spins are entangled and then further neighbors will be entangled respectively. $T_c$ depends on the value of the magnetic field and will be maximized at the quantum critical field.

6 pages, 4 figures

References in corpus (4)

• Experimental quantum teleportation
• Quantum discord and quantum phase transition in spin chains
• Spatially Resolved Detection of a Spin-Entanglement Wave in a Bose-Hubbard Chain
• Thermal entanglement of one-dimensional Heisenberg quantum spin chains in magnetic fields

Cited by in corpus (10)

• Quantum discord and its allies: a review
• Enhancement in performance of quantum battery by ordered and disordered interactions
• Magnetic quantum correlation in the 1D transverse-field XXZ model
• Static and dynamical quantum correlations in phases of an alternating field XY model
• Phase boundaries in alternating field quantum XY model with Dzyaloshinskii-Moriya interaction: Sustainable entanglement in dynamics
• Long range quantum coherence, quantum & classical correlations in Heisenberg XX chain
• Dynamical pairwise entanglement and two-point correlations in the three-ligand spin-star structure
• Probing the Possibilities of Ergodicity in the 1D Spin-1/2 XY Chain with Quench Dynamics
• Entanglement and quantum correlations in the XX spin-$1/2$ honeycomb lattice
• String orders in the Luttinger liquid phase of one-dimensional spin-1/2 systems