Existence of MBL in the thermodynamic limit (general question)

Determine whether many-body localization exists as a bona fide phase or phase transition in the thermodynamic limit in any interacting quantum system, rather than only as an effective finite-size phenomenon at accessible scales.

Background

Beyond the specific SV model, the broader question of MBL’s existence in the thermodynamic limit remains unsettled due to finite-size limitations and potential avalanche-induced delocalization. The authors emphasize that current evidence across platforms supports effective MBL behavior, but not a rigorous thermodynamic phase.

This general open question underlies ongoing debates about the fundamental stability of MBL and the ultimate fate of disordered interacting systems at asymptotically large sizes and times.

References

Therefore, the question of whether MBL exists or not in any system in the thermodynamic limit remains open although MBL certainly exists as an effective phase transition up to very large (perhaps even experimentally relevant) system sizes.

— Many-body Localization in a Slowly Varying Potential  (2503.22096 - Li et al., 28 Mar 2025) in Section V (Conclusion)

If this linear drift persists asymptotically, the crossover would be pushed to arbitrarily strong disorder, implying the absence of a stable MBL phase at any finite $W$. The accessible finite sizes cannot reliably distinguish between these two scaling scenarios and therefore provide no firm basis for establishing or excluding a stable MBL phase, leaving its existence in the thermodynamic limit unresolved.

— Nonlocal Magic across the Many-Body Localization Crossover  (2609.16935 - Li et al., 15 Sep 2026) in Introduction; Section S1, “Numerical methods and conventional MBL diagnostics”

Despite the substantial body of work accumulated since then -- see Refs. for comprehensive reviews -- the fundamental question remains unresolved: does the absence of thermalization survive in the thermodynamic limit, i.e.\ does a genuine many‑body localized phase exist, or is many‑body localization (MBL) merely a finite‑size (or prethermal finite‑time) effect?

— Statistical delocalization in the Anyonic Aubry-André model  (2609.20029 - Agirre et al., 17 Sep 2026) in Section Introduction

In these cases, the FSS procedure actually fails to determine a localization transition. Although $\eta$ and $r$ monotonically drop towards their localized values, the data for different $N$ lacks a clear crossing point, which would be an indicator of a localization transition. This observation clearly underscores the highly delocalizing effect of statistical interactions, while it remains an open question whether this absence of localization transition would also survive in larger systems.

— Statistical delocalization in the Anyonic Aubry-André model  (2609.20029 - Agirre et al., 17 Sep 2026) in Section Results, subsection “Finite-size scaling analysis of spectral observables”; also discussed in Section Discussion

Precise conditions for the stability of the localization in a general interacting system are not yet known.

— Ergodicity in a hole-dopped Anderson spin insulator  (2609.36936 - Bahovadinov et al., 29 Sep 2026) in Section 1, Introduction