Diagonalization and Many-Body Localization for a Disordered Quantum Spin Chain
Mathematical Physics
2016-07-07 v1 Disordered Systems and Neural Networks
math.MP
Spectral Theory
Abstract
We consider a weakly interacting quantum spin chain with random local interactions. We prove that many-body localization follows from a physically reasonable assumption that limits the extent of level attraction in the statistics of eigenvalues. In a KAM-style construction, a sequence of local unitary transformations is used to diagonalize the Hamiltonian by deforming the initial tensor product basis into a complete set of exact many-body eigenfunctions.
Cite
@article{arxiv.1605.03003,
title = {Diagonalization and Many-Body Localization for a Disordered Quantum Spin Chain},
author = {John Z Imbrie},
journal= {arXiv preprint arXiv:1605.03003},
year = {2016}
}
Comments
5 pages, 1 figure. To appear in Phys. Rev. Lett