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

Abstract

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 highdimensional semiconductors. Our model hosts quasiparticles with the dispersion ±|k| α sign 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 renormalisationgroup 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. :2002.12299v1 [cond-mat.mes-hall] arXiv