论文标题
1D中无情电导的非安德森临界缩放
Non-Anderson critical scaling of the Thouless conductance in 1D
论文作者
论文摘要
我们在数值上提出并研究了一个一维模型，该模型表现出非人物疾病驱动的过渡。在Weyl半学，具有远距离跳跃和高维半导体的一维系统的背景下，此类过渡引起了很多关注。我们的模型将带有分散$ \ pm | k |^α\ mathrm {signrm {sign} k $带有$α<1/2 $的质量粒子在动量空间中接近两个点（节点），并包含与短距离相关的随机电势，并允许在节点和每个节点附近散射。与先前研究的模型$ d <3 $相反，此处考虑的模型表现出无关电导的临界缩放，这允许{准确的}确定非安德森过渡的关键特性，精确度显着超过了从状态的关键缩放状态获得的结果，通常在此类过渡中模拟。 We find that in the limit of the vanishing parameter $\varepsilon=2α-1$ the correlation-length exponent $ν=2/(3|\varepsilon|)$ at the transition is inconsistent with the prediction $ν_{RG}=1/|\varepsilon|$ of the perturbative renormalisation-group analysis.我们的结果允许对非生物障碍驱动的过渡的$ \ varepsilon $扩展的收敛性进行数值验证，并且通常，相互作用的领域理论接近临界维度。
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 $\pm |k|^α\mathrm{sign} k$ 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 $\varepsilon=2α-1$ the correlation-length exponent $ν=2/(3|\varepsilon|)$ at the transition is inconsistent with the prediction $ν_{RG}=1/|\varepsilon|$ of the perturbative renormalisation-group analysis. Our results allow for a numerical verification of the convergence of $\varepsilon$-expansions for non-Anderson disorder-driven transitions and, in general, interacting field theories near critical dimensions.
