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Quantum Fisher information and spin squeezing in the ground state of the \(XY\) model. (English) Zbl 1267.81202

Summary: We analyze the quantum Fisher information (QFI) and entanglement of the ground state for the \(XY\) model. The QFI determines the precision in parameter estimations, moreover, it is a criterion of entanglement. The scaling behaviors of the QFI are studied both at the critical point and in different phases. In the symmetry-broken phase, the QFI scales proportional to the square of the system size, while in the symmetric phase, it is nearly independent of the system size. The study of QFI not only reveals the distinct entanglement properties of the \(XY\) model in different phases, but also shows that the ground state of the \(XY\) model can be used to perform Heisenberg-limit parameter estimation.

MSC:

81R30 Coherent states
94A17 Measures of information, entropy
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
81P40 Quantum coherence, entanglement, quantum correlations
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