  The ground state entanglement of the system, both in discrete-time and
continuous-time cases, is quantified through the linear entropy. The result
shows that the entanglement increases as the interaction between the particles
increases in both time scales. It is also found that the strength of the
harmonic potential affects the formation rate of the entanglement of the
system. The different feature of the entanglement between continuous-time and
discrete-time scales is that, for discrete-time entanglement, there is a
cut-off condition. This condition implies that the system can never be in a
maximally entangled state.
