On Many-Body Localization for Quantum Spin Chains

2014/03/31 by John Z. Imbrie · 4 citations
Physics and Astronomy · Mathematics · #math-ph #cond-mat.dis-nn #math.MP #math.PR #msc:82D30 #msc:60K35 #msc:82B44

paper · pdf · doi:10.1007/s10955-016-1508-x

published as Jour. Stat. Phys. 163:998-1048 (2016) · 62 pages, 4 figures, additional details in section 4 and references for published version. To appear in Jour. Stat. Phys

arxiv created 2016/03/30 · arxiv updated 2016/07/08

Abstract

For a one-dimensional spin chain with random local interactions, we prove that many-body localization follows from a physically reasonable assumption that limits the amount of level attraction in the system. The construction uses a sequence of local unitary transformations to diagonalize the Hamiltonian and connect the exact many-body eigenfunctions to the original basis vectors.

Cited by

• Effective and Floquet Hamiltonians for High Frequency Driving and Floquet-induced Heating in Quantum Spin Chains
• Tunable many-body burst in isolated quantum systems
• Emergent Replica Clock Unifies Many-Body Localization and Thermalization
• Length-resolved Operator Growth and Path-Entropy Obstructions to Many-Body Localization

Related

• Aspects of the Mathematical Theory of Disordered Quantum Spin Chains
• The many-body localization transition
• Unified theory of local integrals of motion
• Many-body localization edge in the random-field Heisenberg chain
• The many-body localization phase transition