Critical behavior of the XY spin chain with three-site interaction studied in terms of the Loschmidt echo

Abstract

The effect of the three-site interaction (α) on the critical behaviors of the XY spin chain is studied in terms of the Loschmidt echo (LE). The critical lines can be shifted by α, and the anisotropy parameter of the XY chain has no effect on the critical lines. The scaling behaviors of the LE reveal that the dynamical behaviors of the LE are reliable for characterizing quantum phase transition (QPT).

Decoherence Induced by the Environment for Dimerized Anisotropic XY Spin Chain

“…The decay of coherence is characterized by the Loschmidt echo (LE) which first appears in the context of quantum chaos. The properties of the Loschmidt echo have been extensively investgated in various spin-bath environments such as XY spin chain [8,10], XY spin chain with three-site interaction [11], many-body system with two XY spin chain [12], time-dependent spin chain [13], etc. These reseaches reveal some connections between the enhanced decoherence of the Loschmidt echo and quantum phase transitions.…”

Loschmidt Echo of a central spin coupled to an XY spin chain: The role of the Dzyaloshinsky-Moriya interaction

“…Recently, we have discussed the critical behaviors of an XY spin chain with different interactions in terms of the LE, including the three-site interaction [28][29][30] and DM interaction [31]. In the work of Ref.…”