Diagonalization and Many-Body Localization for a Disordered Quantum Spin Chain

TL;DR

This paper demonstrates that many-body localization in a disordered quantum spin chain can be rigorously proven using a KAM-style approach, under assumptions limiting eigenvalue level attraction.

Contribution

It introduces a novel proof of many-body localization for disordered quantum spin chains using a KAM-style diagonalization method under physically reasonable assumptions.

Findings

Proves many-body localization under specific eigenvalue statistics assumptions.

Develops a KAM-style local unitary transformation technique for diagonalizing the Hamiltonian.

Establishes a rigorous connection between level statistics and localization phenomena.

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.