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International Journal of Quantum Information

ENTANGLEMENT MODULATION IN A SPIN CHAIN BY A LOCAL IMPURITY

Tony J. G. Apollaro, Alessandro Cuccoli, Andrea Fubini, Francesco Plastina, Paola Verrucchi

Published Jul 1, 2008• 4 citations
Publisher

Abstract

We study the ground-state entanglement properties of an XX spin 1/2 chain in transverse field, in its quasi-long-ranged ordered phase, with a magnetic impurity, represented in terms of an additional transverse magnetic field located at one precise site. For such a system, we show that a control of the ground state entanglement can be achieved by acting on the impurity field. To demonstrate this possibility, we evaluate exactly the nearest neighbor and next-nearest neighbor concurrence in the presence of the impurity. It turns out that either an enhancement or a quenching of entanglement between selected spin pairs can be obtained by acting on the intensity of the impurity. For specific values of the magnetic field a spatial modulation of concurrence along the chain is also obtained.

DOI
10.1142/s0219749908003797

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We study the ground-state entanglement properties of an XX spin 1/2 chain in transverse field, in its quasi-long-ranged ordered phase, with a magnetic impurity, represented in terms of an additional transverse magnetic field located at one precise site. For such a system, we show that a control of the ground state entanglement can be achieved by acting on the impurity field. To demonstrate this possibility, we evaluate exactly the nearest neighbor and next-nearest neighbor concurrence in the presence of the impurity. It turns out that either an enhancement or a quenching of entanglement between selected spin pairs can be obtained by acting on the intensity of the impurity. For specific values of the magnetic field a spatial modulation of concurrence along the chain is also obtained.
We study the effects of an impurity on the magnetic response and the entanglement properties of the infinite S=1/2 XX chain in a transverse field h in its quasi-long-range ordered phase, i.e., below the critical point h=1. We show that regardless of the sign of the exchange coupling, and for whatever value of the applied field, the impurity generates an oscillating magnetization that displays a power-law decay with the distance from the impurity itself. This effect sensibly modifies the overall magnetic behavior of the chain, as testified by the observed rounding-off of the divergence of the longitudinal susceptibility. Moreover, the emergence of the above alternating structure in the spin configuration entails a substantial change in the pairwise entanglement distribution along the chain, so that concurrences are found either enhanced (up to a factor larger than 2) or quenched, depending on the distance of the spin pair from the impurity, on its strength, and on the value of the magnetic field. Acting on such control parameters, an adiabatic manipulation of both the magnetic and entanglement properties can be performed. We find these effects robust against thermal fluctuations, and we can therefore suggest realistic setups to experimentally probe the predicted behavior.
We study the effects of an impurity on the magnetic response and the entanglement properties of the infinite S=12S=\frac{1}{2}S=21​ XXXXXX chain in a transverse field hhh in its quasi-long-range ordered phase, i.e., below the critical point h=1h=1h=1. We show that regardless of the sign of the exchange coupling, and for whatever value of the applied field, the impurity generates an oscillating magnetization that displays a power-law decay with the distance from the impurity itself. This effect sensibly modifies the overall magnetic behavior of the chain, as testified by the observed rounding-off of the divergence of the longitudinal susceptibility. Moreover, the emergence of the above alternating structure in the spin configuration entails a substantial change in the pairwise entanglement distribution along the chain, so that concurrences are found either enhanced (up to a factor larger than 2) or quenched, depending on the distance of the spin pair from the impurity, on its strength, and on the value of the magnetic field. Acting on such control parameters, an adiabatic manipulation of both the magnetic and entanglement properties can be performed. We find these effects robust against thermal fluctuations, and we can therefore suggest realistic setups to experimentally probe the predicted behavior.
We consider a finite two dimensional XY spin model. The model consists of a set of seven localized spin- 12 particles in a two dimensional triangular lattice coupled through nearest neighbor exchange interaction in presence of an external magnetic field. We study the effect of a single impurity spin coupled to its nearest neighbor through an exchange interaction J′ on the pairwise entanglement between the different spins in the lattice. We found that when the spin is located at a border site the entanglement between the impurity and its nearest neighbors increases monotonically with J′ reaching a saturation value that depends on the magnetic field strength h. On the other hand the entanglement with the next nearest spins shows a critical behavior where the entanglement increases and then decreases rapidly until it vanishes. The critical coupling value at which the entanglement vanishes increases as h increases. Studying the entanglement between two spins excluding the impurity show that while the entanglement between two spins coupled to the impurity reach a saturation value as J′ increases, it vanishes for spins not coupled to the impurity. Furthermore studying the effect of a central impurity show that the entanglement between nearest neighbor and next nearest neighbor spins reaches an asymptotic value as J′ increases. Interestingly it was demonstrated that the impurity can be used as a switch to control the entanglement between different spins in the lattice turning it on and off.
For a three-qubit Heisenberg model in a uniform magnetic field, the pairwise thermal entanglement of any two sites is identical due to the exchange symmetry of sites. In this paper we consider the effect of a non-uniform magnetic field on the Heisenberg model, modelling a magnetic impurity on one site. Since pairwise entanglement is calculated by tracing out one of the three sites, the entanglement clearly depends on which site the impurity is located. When the impurity is located on the site which is traced out, that is, when it acts as an external field of the pair, the entanglement can be enhanced to the maximal value 1; while when the field acts on a site of the pair the corresponding concurrence can only be increased from 1/3 to 2/3.
The zero-temperature pairwise entanglement is investigated in the antiferromagnetic Heisenberg chain with one impure spin s. The impurity location is varied from the open end to a mediate site of the spin chain. It is found that the pairwise entanglement is proportional to 1/s. This means that the entanglement will disappear in the classical systems as s → ∞. Compared to the isotropic Heisenberg chain without impurity, the efficient control of the spin coupling between the impurity spin and nearest-neighbor spins can enhance the pairwise entanglement.
Using the method of the Jordan–Wigner transformation for solving different spin–spin correlation functions, we have investigated the generation of next-nearest-neighbouring entanglement in a one-dimensional quantum Ising spin chain with the Gaussian distribution impurities of exchange couplings and external magnetic fields taken into account. The maximal value of entanglement between the next-nearest-neighbouring qubits in the transverse Ising model was analysed in detail by varying the effectively controlled parameters such as interchange coupling, magnetic field and the system impurity. For such systems, where both exchange couplings and external magnetic field disorder appear, we show that it is possible to achieve next-nearest-neighbouring entanglement better than the previously discussed pure Ising spin chain case. We also show that the Gaussian distribution impurity can induce next-nearest-neighbouring entanglement, which can be used as a means to characterize quantum phase transition.