2025/12/03 by Lorenzo Tonetti, Leticia F. Cugliandolo, Tonetti, Lorenzo +3
Physics and Astronomy · #Anderson localization #Bethe lattice #Critical exponent #Criticality #Lattice (music) #Percolation (cognitive psychology) #Percolation critical exponents #Quantum and electron transport phenomena #Quantum many-body systems #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.2512.04037
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2025/12/03 · openalex created_date 2025/12/05 · openalex updated_date 2026/07/28
The Localization Landscape Theory (LLT) provides a classical picture of Anderson localization by introducing an effective confining potential whose percolation is proposed to coincide with the mobility edge. Although this proposal shows remarkable numerical agreement in three dimensions, its fundamental validity remains unsettled. Here we test the LLT analytically on the Bethe lattice, where both the Anderson localization transition and the LLT percolation problem are exactly solvable. We find that the two transitions do not coincide, and their critical behaviors differ markedly. In particular, LLT percolation displays standard mean-field percolation criticality that is fundamentally distinct from the peculiar critical behavior of the Anderson transition on the Bethe lattice. Our results provide an exact benchmark showing that, while geometrically intuitive, the LLT does not capture the true quantum critical properties of localization.