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In this paper, the critical behavior of the general XY spin chain with the Dzyaloshinsky–Moriya (DM) interaction is studied by means of a Loschmidt Echo (LE) calculation. LE presents a Gauss decay in the region of magnetic field intensity |λ|<1 and an exponential decay in the region of |λ|>1. There exists a critical spin chain size N C . When spin chain size is larger than N C ...
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