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Area law in the exact solution of many-body localized systems
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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.
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Dynamics and Transport at the Threshold of Many-Body Localization
A review organizing nearly many-body-localized systems around a common picture of localized degrees of freedom coupled to slow, nontrivial thermal baths.
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