Non-Markovian Dynamic for a single-particle in spin-1/2 chain

The dynamical behavior of spin 1/2 XX type of Heisenberg chain in presence of cluster interaction is considered. Using Fermionization method, the Hamiltonian of the chain system is diagonalized and energy spectrum is obtained. One particle of the chain is selected as an open quantum. The initial state is considered as a superposition of two states of the spin-1/2 particle. We have shown that the dynamics of the mentioned single-particle system is non-Markov for all range values of the cluster interaction.