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Register a new userGenerando entrelazamiento en cadenas XY - (Generating entanglement in XY chains)
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Added by
Christian Tom\\'as Schmiegelow
Publication date
2006
fields
Physics
and research's language is
English
Authors
C. T. Schmiegelow
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Se estudia en este trabajo la capacidad de generar entrelazamiento de una cadena de espines con acoplamiento de Heisenberg XY y un campo magnetico uniforme a partir de un estado inicial en el que los espines estan completamente alineados. Se encuentra que la capacidad de generar estados entrelazados no muestra un comportamiento monotono con el campo presentando, en cambio, plateaus y resonancias. Tambien se muestra que, a pesar de que la anisotropia es necesaria para que se generen estados entrelazados, una mayor anisotropia no implica necesariamente mejores condiciones para generar entrelazamiento que sirva para usarse en una computadora cuantica. Inclusive, se observa que, se genera una cantidad finita de entrelazamiento en el limite de pequena anisotropia. (The maximum entanglement reached by an initially fully aligned state evolving in a XY Heisenberg spin chain placed in a uniform transverse magnetic field is studied. It is shown that the capacity to create entangled states (both of one qubit with the rest of the chain and pairwise between two adjacent qubits) is not a monotonous function of the magnetic field: it presents plateaus and resonances. It is also shown that, though anisotropy in the interaction is necessary for entanglement generation, the best conditions for generating entanglement that may be suitable for use in quantum computation is not that of biggest anisotropy. Moreover finite amounts of entanglement are generated in the small anisotropy limit.)
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We study the creation and distribution of entanglement in disordered $XY$-type spin-$1/2$ chains for the paradigmatic case of a single flipped spin prepared on a fully polarized background. The local magnetic field is set to follow a disordered long-range-correlated sequence with power-law spectrum. Depending on the degree of correlations of the disorder, a set of extended modes emerge in the middle of the band yielding an interplay between localization and delocalization. As a consequence, a rich variety of entanglement distribution patterns arises, which we evaluate here through the concurrence between two spins. We show that, even in the presence of disorder, the entanglement wave can be pushed to spread out reaching distant sites and also enhance pairwise entanglement between the initial site and the rest of the chain. We also study the propagation of an initial maximally-entangled state through the chain and show that correlated disorder improves the transmission quite significantly when compared with the uncorrelated counterpart. Our work contributes in designing solid-state devices for quantum information processing in the realistic setting of correlated static disorder.
It has been shown that, for the two-qubit Heisenberg XY model, anisotropy and magnetic field may together be used to produce entanglement for any finite temperature by adjusting the external magnetic field beyond some finite critical strength. This interesting result arises from an analysis employing the Wootters concurrence, a computable measure of entanglement for two-qubit states. Recently, Mintert {em et al.} proposed generalizations of Wootters concurrence for multipartite states. These MKB concurrences possess a mathematical property that enables one to understand the origin of this characteristic behavior. Here, we first study the effect of anisotropy and magnetic field on the multipartite thermal entanglement of a four-qubit Heisenberg XY chain using the MKB concurrences. We show that this model exhibits characteristic behavior similar to that of the two-qubit model. In addition, we show that this can again be understood using the same mathematical property. Next, we show that the six-qubit Heisenberg XY chain possesses properties necessary for it to have the characteristic behavior too. Most importantly, it is possible to directly measure the multipartite MKB concurrences of pure states. This may provide an experimental verification of our conjecture that for a Heisenberg XY chain of any even number of qubits, it is always possible to obtain non-zero genuine multipartite entanglement at any finite temperature by applying a sufficiently large magnetic field.
We analyze the bipartite and multipartite entanglement for the ground state of the one-dimensional XY model in a transverse magnetic field in the thermodynamical limit. We explicitly take into account the spontaneous symmetry breaking in order to explore the relation between entanglement and quantum phase transitions. As a result we show that while both bipartite and multipartite entanglement can be enhanced by spontaneous symmetry breaking deep into the ferromagnetic phase, only the latter is affected by it in the vicinity of the critical point. This result adds to the evidence that multipartite, and not bipartite, entanglement is the fundamental indicator of long range correlations in quantum phase transitions.
We investigate the entanglement of the ferromagnetic XY model in a random magnetic field at zero temperature and in the uniform magnetic field at finite temperatures. We use the concurrence to quantify the entanglement. We find that, in the ferromagnetic region of the uniform magnetic field $h$, all the concurrences are textit{generated} by the random magnetic field and by the thermal fluctuation. In one particular region of $h$, the next-nearest neighbor concurrence is generated by the random field but not at finite temperatures. We also find that the qualitative behavior of the maximum point of the entanglement in the random magnetic field depends on whether the variance of its distribution function is finite or not.
In this study, considering the long-range interaction with an inverse-square and its trigonometric and hyperbolic variants in SCM model we investigate entanglement in (1/2,1) mixed-spin XY model. We also discuss the temperature and magnetic field dependence of the thermal entanglement in this system for different types of interaction. The numerical results show that, in the presence of the long-range interactions, thermal entanglement between spins has a rich behavior dependent upon the interaction strength, temperature and magnetic field. Indeed we find that for less than a critical distance there are entanglement plateaus dependent upon the distance between the spins, whereas above the critical distance the entanglement can exhibit sudden death.
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