Universality class of deterministic MBL transitions (QP vs SV and beyond)

Determine whether all deterministic one-dimensional models that exhibit many-body localization transitions—such as quasiperiodic and slowly varying potential models—belong to a single universality class characterized by the same critical behavior (e.g., critical exponent ν), or whether these deterministic systems form multiple distinct universality classes.

Background

The authors compute an effective critical exponent ν≈2 for the slowly varying (SV) model and compare it to ν≈2.4 reported for quasiperiodic (QP) models, both of which differ from the larger exponent observed for random-disorder models. This suggests possible commonality between SV and QP transitions, but the small discrepancy leaves room for distinct classes.

They explicitly note that it is not clear whether all deterministic models (including QP and SV) share a single universality class. This motivates a precise classification of universality across deterministic MBL transitions.