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arXiv:1501.05004 · Journal of Physics B Atomic Molecular and Optical Physics

Quantum uncertainty in critical systems with three spins interaction

Thiago Mureebe Carrijo, Ardiley Torres Avelar, Lucas C. Céleri

Published May 19, 2015• 14 citations
arXivHTMLPDF

Abstract

Abstract In this article we consider two spin-1/2 chains described, respectively, by the thermodynamic limit of the XY model with the usual two site interaction, and an extension of this model (without taking the thermodynamics limit), called XYT , were a three site interaction term is presented. To investigate the critical behaviour of such systems we employ tools from quantum information theory. Specifically, we show that the local quantum uncertainty, a quantity introduced in order to quantify the minimum quantum share of the variance of a local measurement, can be used to indicate quantum phase transitions presented by these models at zero temperature. Due to the connection of this quantity with the quantum Fisher information, the results presented here may be relevant for quantum metrology and quantum thermodynamics.

DOI
10.1088/0953-4075/48/12/125501

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We study the relationship between the quantum Fisher information (QFI) of spin pairs and the topological quantum phase transitions (TQPTs) of the extended XY model driven by the anisotropies of the nearest-neighbor and the next-nearest-neighbor spins, the transverse magnetic field, and the three-spin interaction. We find that the first derivative of QFI can correctly characterize the TQPTs at absolute zero temperature. Meanwhile, the impacts of the thermal fluctuations and the site distance of spin pairs on the critical behaviors of the QFI are studied. It is found that the first derivative of QFI for the nearest neighbor or the long-distance spin pairs can only correctly characterize the critical points of the TQPTs at sufficiently low temperature. Remarkably, when the anisotropy of the nearest-neighbor and the next-nearest-neighbor spins are the driven parameters and the site distance R=5R=5R=5, the QFI itself can characterize the TQPTs at absolute zero temperature.
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