Tuning entanglement and ergodicity in two-dimensional spin systems using impurities and anisotropy

Abstract

We consider the entanglement in a two dimensional XY model in an external magnetic field h. The model consists of a set of 7 localized spin-1 2 particles in a two dimensional triangular lattice coupled through nearest neighbor exchange interaction J. We examine the effect of single and double impurities in the system as well as the degree of anisotropy on the nearest neighbor entanglement and ergodicity of the system. We have found that the entanglement of the system at the different degrees of anisotropy mimics that of the one dimensional spin systems at the extremely small and large values of the parameter λ = h/J. The entanglement of the Ising and partially anisotropic system show phase transition in the vicinity of λ = 2 while the entanglement of the isotropic system suddenly vanishes there. Also we investigate the dynamic response of the system containing single and double impurities to an external exponential magnetic field at different degrees of anisotropy. We have demonstrated that the ergodicity of the system can be controlled by varying the strength and location of the impurities as well as the degree of anisotropy of the coupling.

Ground State, Magnetization Process and Bipartite Quantum Entanglement of a Spin-1/2 Ising–Heisenberg Model on Planar Lattices of Interconnected Trigonal Bipyramids

“…The low-dimensional Heisenberg spin models, involving quantum fluctuations between spins, play a significant role in this regard because they have been proven to be ideal candidates for a rigorous investigation of the entangled states under the influence of the external stimuli such as magnetic field (homogeneous or inhomogeneous) and/or temperature [ 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 ]. Moreover, many analytical and numerical calculations have been performed to examine the tuning of the quantum and thermal bipartite entanglement by varying the exchange anisotropy parameter [ 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 ], the uniaxial single-ion anisotropy [ 16 , 17 ], the Dzyaloshinskii–Moriya interaction (spin-orbit coupling) [ 18 , 19 , 20 , 26 , 27 ], the next-nearest-neighbour interaction [ 13 , 14 , 29 ], as well as by introducing impurities into the system [ 28 , 30 ].…”

Ground State, Magnetization Process and Bipartite Quantum Entanglement of a Spin-1/2 Ising-Heisenberg Model on Planar Lattices of Interconnected Trigonal Bipyramids

“…The low-dimensional Heisenberg spin models, involving quantum fluctuations between spins, play a significant role in this regard because they have been proven to be ideal candidates for a rigorous investigation of the entangled states under the influence of the external stimuli such as magnetic field (homogeneous or inhomogeneous) and/or temperature [12][13][14][15][16][17][18][19][20][21][22][23][24]. Moreover, many analytical and numerical calculations have been performed to examine the tuning of the quantum and thermal bipartite entanglement by varying the exchange anisotropy parameter [19][20][21][22][23][24][25][26][27][28], the uniaxial single-ion anisotropy [16,17], the Dzyaloshinskii-Moriya interaction (spin-orbit coupling) [18-20, 26, 27], the next-nearestneighbour interaction [13,14,29], as well as by introducing impurities into the system [28,30].…”

Central symmetry in two-dimensional lattices and quantum information transmission

“…Entanglement properties in a two-dimensional triangular lattice with impurities are investigated in Refs. [17] and [18], where Ising and XY-type interactions are considered, respectively. Experimentally it is hard to realize the required nonuniform couplings between sites, whereas uniform couplings between spin sites are much more feasible with state-of-the-art technologies.…”