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By means of the Loschmidt Echo (LE) and Berry Phase (BP) calculations, quantum phase transition (QPT) of an XY spin chain with three-site interaction (α) in a transverse magnetic field (λ) is studied. Both the LE and BPʼs λ derivative present anomaly behaviors at the critical regions λ1,λ2 and λ3. The model is in the Ferromagnetic phase as λ>λ1=1+α and in the Spin Liquid I phase as −1+α<λ<1+α...
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