Non-Anderson critical scaling of the Thouless conductance in 1D

摘要

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 +/-vertical bar k vertical bar(alpha) sign k with alpha < 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 epsilon = 2 alpha - 1 the correlation-length exponent v = 2/(3 vertical bar epsilon vertical bar) at the transition is inconsistent with the prediction v(RG) = 1/vertical bar epsilon&VERBAR of the perturbative renormalisation-group analysis. Our results allow for a numerical verification of the convergence of epsilon-expansions for non-Anderson disorder-driven transitions and, in general, interacting field theories near critical dimensions. (C) 2020 Elsevier Inc. All rights reserved.