Thermodynamic-limit MBL in the slowly varying potential (SV) model

Establish whether many-body localization exists as a true thermodynamic phase transition in the interacting one-dimensional slowly varying potential model with nearest-neighbor hopping, on-site potential U_j = λ cos(π α j^s + φ) for 0 < s < 1, and nearest-neighbor interaction V, i.e., determine if localization persists in the infinite-size and infinite-time limits rather than only as an effective finite-size phenomenon.

Background

The paper studies many-body localization (MBL) in a deterministic one-dimensional model with a slowly varying potential and nearest-neighbor interactions. Using exact diagonalization and a real-space renormalization group (RG), the authors find clear signatures of an MBL-to-ergodic transition and effective critical behavior up to large system sizes (L up to 1000).

However, the authors emphasize that their analysis (as with prior work on random and quasiperiodic systems) addresses effective transitions at accessible sizes and does not rigorously establish a thermodynamic phase transition. The question remains open whether the SV model exhibits a bona fide MBL phase transition in the thermodynamic limit, especially in light of potential avalanche instabilities.