Many-body localization
For a specified ensemble of interacting disordered spin chains, establish or exclude thermodynamic many-body localization with a stated energy window, probability bound and quasilocal-integral-of-motion criterion. Determine stability under a bounded local pert
Problem statement
For a specified ensemble of interacting disordered spin chains, establish or exclude thermodynamic many-body localization with a stated energy window, probability bound and quasilocal-integral-of-motion criterion. Determine stability under a bounded local perturbation class; treat higher-dimensional avalanche instability separately.
Lean 4
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Background
Many-body localization (MBL) is the conjectured survival of Anderson localization once interactions are switched on: an isolated, strongly disordered interacting system fails to thermalize, retains memory of initial conditions, and exhibits an emergent set of quasilocal integrals of motion (l-bits) with only logarithmic entanglement growth.
What is known: The strongest rigorous result is Imbrie's proof of MBL for a specific disordered 1D quantum spin chain, conditional on a physically reasonable but unproven level-statistics (limited level attraction) assumption. Perturbative and numerical studies broadly support an MBL phase in strongly disordered 1D systems.
The status is genuinely contested. De Roeck and Huveneers develop an ETH-based avalanche theory: rare thermal regions may destabilize localization, with particularly severe higher-dimensional predictions. This is not an unconditional theorem excluding every MBL model. Finite-size drifts make numerical extrapolation difficult. A rigorous result must state its disorder law, interaction strengths, energy window, localization diagnostic and perturbation norm; absence of fast transport at accessible sizes does not itself prove a stable thermodynamic phase. Related: B4, B7, U3.
Progress & source assessment
Source catalogue review: 4 September 2026. Improved indicates partial progress, including qualified preprint claims.
- [1]Imbrie, 'On many-body localization for quantum spin chains', J. Stat. Phys. 163 (2016) link
- [2]De Roeck & Huveneers, 'Stability and instability towards delocalization in MBL systems', PRB 95, 155129 (2017) link
- [3]Abanin, Altman, Bloch, Serbyn, 'Many-body localization, thermalization, and entanglement', Rev. Mod. Phys. 91, 021001 (2019) link
Recorded progress
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