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

TL;DR

This paper proves an area law for entanglement in many-body localized systems using a class of unitaries with quasi-local structure, extending previous proofs and connecting to Lieb-Robinson bounds.

Contribution

It introduces a broader class of unitaries to establish an independent proof of the area law in MBL eigenstates, linking to Lieb-Robinson bounds and Hamiltonian diagonalization.

Findings

Bound entanglement for states generated by quasi-local unitaries.

Provided an error estimate for finite-depth local circuit approximations.

Connected the structure of unitaries to Lieb-Robinson bounds and Hamiltonian diagonalization.

Abstract

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.