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A thermodynamic limit chain of spin-1/2 particles with XX and three-spininteractions (TSI) is considered. Using the fermionization technique, theHamiltonian of the chain with periodic boundary conditions is exactlydiagonalized. In the ground-state phase diagram of the chain system, a quantumcritical point separates the Luttinger liquid and chiral phases. Selectingone-spin as an open quantum system, the rest of the spins play the role of itsenvironment. By choosing different initial states, we studied the dynamics ofthe entanglement between the open quantum system and its environment. In theinitial state, the state of the open quantum system is a superposition of upand down states and the environment is polarized. The revival of theentanglement is observed in the whole range of interactions as an indicator ofnon-Markovian dynamics. Our exact results revealed that non-Markovian behavioris independent of the initial state. By tuning the initial state, the openquantum system will be completely entangled with the environment at a specialtime called entanglement-time, tE. The value of the mentioned entanglement-timedecreased by increasing TSI. The signature of a quantum critical point isconfirmed by investigating the long-time average of the entanglement and usingthe trace-distance as a witness of non-Markovianity.

Signature of the quantum critical point on the witness of the non-Markovianity and the entanglement in spin-1/2 chain