Quantum Entanglement in Spin Dimers: Effects of a Magnetic Field and Heterogeneous g-Factors
- PDF / 464,855 Bytes
- 7 Pages / 612 x 792 pts (letter) Page_size
- 70 Downloads / 268 Views
tum Entanglement in Spin Dimers: Effects of a Magnetic Field and Heterogeneous g-Factors Z. A. Adamyana, b, *, S. A. Muradyana, and V. R. Ohanyana aYerevan
b
State University, Yerevan, Armenia CANDLE Synchrotron Research Institute, Yerevan, Armenia *e-mail: [email protected]
Received February 27, 2020; revised March 29, 2020; accepted April 10, 2020
Abstract—This work considers the spin-1/2 Heisenberg dimer, the mixed spin-(1/2,1) Heisenberg dimer and their quantum entanglement, particularly, the dependence of the entanglement on the system characteristics and the external magnetic field. The quantum entanglement in this work is determined using two different methods, namely ‘Negativity’ and ‘Concurrence’. The dependence of the corresponding quantities on spins Landé g-factors, system anisotropy constants and exchange constant is discussed. Keywords: quantum entanglement, phase transitions, spin, magnetic field, Landé multipliers DOI: 10.3103/S1068337220040027
1. INTRODUCTION Quantum entanglement, as one of the most intriguing features of quantum theory, has recently attracted more and more attention, because it is a valuable resource in quantum communication and information processing [1–5]. It underlies the schemes of quantum teleportation [6–11], quantum computing [12–14], and quantum cryptography [15–17]. On the other hand, the understanding of quantum entanglement has led to progress in studying the properties of black holes using quantum field theory methods. Moreover, entanglement provides a new perspective for understanding quantum phase transitions and collective phenomena in many-body and condensed matter physics. According to Schrödinger, entanglement is perhaps the most fundamental characteristic that distinguishes quantum physics from the classical world. The Heisenberg spin chain systems provide fairly convenient conditions for creating and controlling entangled states [18–21]. In this work, we consider two systems of the Heisenberg model: spin-1/2 completely anisotropic XYZ dimer with two different but isotropic Landé g-factors, and Z anisotropic dimer with mixed spin- (1/2,1). This work solves the problem of finding the optimal parameters to create entangled states and control them by means of a magnetic field. 2. THE MAIN CHARACTERISTICS OF THE SYSTEMS STUDIED 2.1. The Heisenberg Spin-1/2 Two-Particle System For a spin-1/2 two-particle system, the Hamiltonian will have the following form [25]:
H = J ((1 + γ)S1x S2x + (1 − γ)S1y S2y + ΔS1z S2z ) + Dz (S1x S2y − S1y S2x ) − B( g1S1z + g2S2z ),
(1)
x, y, z where S1,2 are the components of the spin-1/2 operator, g1 g2 are Landé g-factors, respectively, of the first and second particles, J is the exchange interaction between particles, Δ and γ are constants, Z and XY are anisotropies, the magnetic field B is directed along the z axis. For the eigenvalues and eigenfunctions of the Hamiltonian, we have the following expressions
ε1,2 = − J Δ 1 B 2 g −2 + Dz2 + J 2, 4 2 292
(2)
QUANTUM ENTANGLEMENT IN SPIN DIMERS
E/J
293
E4
5 E2 0 E1 –5
Data Loading...
