  We consider a chain of spin-half particles of a finite length, evolved with
the mixed-field Ising Hamiltonian and impose open boundary condition. We
simulate the time evolution of entanglement entropy and mutual information
following quench from the N\'eel state in this system using tensor networks. We
find that the entanglement entropy for non-integrable systems saturates to a
constant value at late times, however it continues to oscillate for integrable
systems. We also find that mutual information peaks as a function of distance
between intervals decay faster for non-integrable systems compared to
integrable systems, in agreement with the conclusion of \cite{Alba:2019ybw} for
XXZ chains. We compare the oscillations in entanglement entropy evolution
obtained from simulations in the integrable case with analytic results from
quasi-particle picture and find agreement.
