2020/02/27 by Björn Sbierski, Sergey Syzranov
Physics and Astronomy · #Anderson impurity model #Anderson localization #Condensed matter physics #Conductance #Context (archaeology) #Critical exponent #Critical phenomena #Exponent #Mathematical physics #Phase transition #Physics #Position and momentum space #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Quasiparticle #Scaling #Statistical physics #Superconductivity #Topological Materials and Phenomena #cond-mat.dis-nn #cond-mat.mes-hall #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.1016/j.aop.2020.168169
published as Annals of Physics 418 (2020) 168169 · 12 pages
arxiv created 2020/02/27 · openalex publication_date 2020/04/08 · arxiv updated 2020/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We propose and investigate numerically a one-dimensional model which exhibits a non-Anderson disorder-driven transition. Such transitions have recently been attracting a great deal of attention in the context of Weyl semimetals, one-dimensional systems with long-range hopping and high-dimensional semiconductors. Our model hosts quasiparticles with the dispersion ± |k|αsign k with α<1/2 near two points (nodes) in momentum space and includes short-range-correlated random potential which allows for scattering between the nodes and near each node. In contrast with the previously studied models in dimensions d<3, the model considered here exhibits a critical scaling of the Thouless conductance which allows for an accurate determination of the critical properties of the non-Anderson transition, with a precision significantly exceeding the results obtained from the critical scaling of the density of states, usually simulated at such transitions. We find that in the limit of the vanishing parameter ε=2α-1 the correlation-length exponent ν=2/(3|ε|) at the transition is inconsistent with the prediction νRG=1/|ε| of the perturbative renormalisation-group analysis. Our results allow for a numerical verification of the convergence of ε-expansions for non-Anderson disorder-driven transitions and, in general, interacting field theories near critical dimensions.