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

Abstract: A thermodynamic limit chain of spin-1/2 particles with XX and three-spin interactions (TSI) is considered. Using the fermionization technique, the Hamiltonian of the chain with periodic boundary conditions is exactly diagonalized. In the ground-state phase diagram of the chain system, a quantum critical point separates the Luttinger liquid and chiral phases. Selecting one-spin as an open quantum system, the rest of the spins play the role of its environment. By choosing different initial states, we studied the dynamics of the entanglement between the open quantum system and its environment. In the initial state, the state of the open quantum system is a superposition of up and down states and the environment is polarized. The revival of the entanglement is observed in the whole range of interactions as an indicator of non-Markovian dynamics. Our exact results revealed that non-Markovian behavior is independent of the initial state. By tuning the initial state, the open quantum system will be completely entangled with the environment at a special time called entanglement-time, tE. The value of the mentioned entanglement-time decreased by increasing TSI. The signature of a quantum critical point is confirmed by investigating the long-time average of the entanglement and using the trace-distance as a witness of non-Markovianity.