  A novel method has been devised to compute the Local Integrals of Motion
(LIOMs) for a one-dimensional many-body localized system. In this approach, a
class of optimal unitary transformations is deduced in a tensor-network
formalism to diagonalize the Hamiltonian of the specified system. To construct
the tensor network, we utilize the eigenstates of the subsystems Hamiltonian to
attain the desired unitary transformations. Subsequently, we optimize the
eigenstates and acquire appropriate unitary localized operators that will
represent the LIOMs tensor network. The efficiency of the method was assessed
and found to be both fast and almost accurate. In framework of the introduced
tensor-network representation, we examine how the entanglement spreads along
the considered many-body localized system and evaluate the outcomes of the
approximations employed in this approach. The important and interesting result
is that in the proposed tensor network approximation, if the length of the
blocks is greater than the length of localization, then the entropy growth will
be linear in terms of the logarithmic time. Also, it has been demonstrated
that, the entanglement can be calculated by only considering two blocks next to
each other, if the Hamiltonian has been diagonalized using the unitary
transformation made by the provided tensor-network representation.
