2026/08/04 by A. Östlin, I. Titvinidze, M. Kollar +2
Physics and Astronomy · #cond-mat.dis-nn
12 pages, 7 figures
arxiv created 2026/08/04 · arxiv published 2026/08/04 · arxiv updated 2026/08/05
We present a combined numerical and analytically tractable realization of the typical medium theory (TMT) for Anderson localization on the infinite-connectivity Bethe lattice with Cauchy-distributed on-site disorder. Exploiting the special properties of the Cauchy distribution and the Bethe lattice, we derive an analytical expression for the typical density of states (TDOS) and obtain a simplified TMT self-consistency scheme. We show that the TDOS at the band center decreases linearly with disorder strength and vanishes at the critical disorder Wc=D/2. The resulting ω--W phase diagram reveals the continuous collapse of the mobility edge and the disappearance of extended states.