English

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

Quantum Physics 2017-08-29 v1 Disordered Systems and Neural Networks Mathematical Physics math.MP

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.

Keywords

Cite

@article{arxiv.1708.08069,
  title  = {Area law in the exact solution of many-body localized systems},
  author = {Evgeny Mozgunov},
  journal= {arXiv preprint arXiv:1708.08069},
  year   = {2017}
}

Comments

21 page, 3 figures