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

Area law in the exact solution of many-body localized systems