Avalanche transition in the slowly varying potential model

Ascertain whether an avalanche stability transition point exists in the interacting one-dimensional slowly varying potential model with on-site potential U_j = λ cos(π α j^s + φ) (0 < s < 1), and, if it exists, identify and characterize this transition controlling delocalization via many-body resonances.

Background

Avalanche mechanisms are known to destabilize MBL in random and quasiperiodic systems by enabling large thermal regions to grow and thermalize the system. The RG scheme used here does not explicitly include such avalanches, though upward drifts in apparent critical points with system size suggest possible instability.

The authors explicitly state uncertainty about the existence of a distinct avalanche transition point in the SV model, making it an explicit open problem to determine if, where, and how such a transition occurs.