  Many-body localization was proven under realistic assumptions by constructing
a quasi-local unitary rotation that diagonalizes the Hamiltonian (Imbrie,
2016). A natural generalization is to consider all unitaries that have a
similar structure. We bound entanglement for states generated by such
unitaries, thus providing an independent proof of area law in eigenstates of
many-body localized systems. An error of approximating the unitary by a
finite-depth local circuit is obtained. We connect the defined family of
unitaries to other results about many-body localization (Kim et al, 2014), in
particular Lieb-Robinson bound. Finally we argue that any Hamiltonian can be
diagonalized by such a unitary, given it has a slow enough logarithmic
lightcone in its Lieb-Robinson bound.
