Quantum phase transition in XY spin chain with three-site interaction studied in terms of Loschmidt echo and Berry phase

摘要

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 BP's 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. ~(λ1) and ~(λ2) are independent on the anisotropy parameter γ. But, the anisotropy interaction can shift the critical line ~(λ3) between the Spin Liquid II phase and the Ferromagnetic phase. The present work suggests that QPT of the XY spin chain with three-site interaction can be characterized by exploring the dynamical behaviors of the LE and BP.