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 $\pm |k|^\alpha \mathrm{sign} k$ 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 $\varepsilon=2\alpha-1$ the correlation-length exponent $\nu=2/(3|\varepsilon|)$ at the transition is inconsistent with the prediction $\nu_{RG}=1/|\varepsilon|$ 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.

中文翻译：

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一维中 Thouless 电导的非安德森临界缩放

我们提出并在数值上研究了一个一维模型，该模型展示了非安德森无序驱动的转变。这种转变最近在外尔半金属、具有长距离跳跃的一维系统和高维半导体的背景下引起了极大的关注。我们的模型在动量空间中的两个点（节点）附近托管具有色散 $\pm |k|^\alpha \mathrm{sign} k$ 的准粒子，其中 $\alpha<1/2$ 并且包括短程相关的随机势这允许节点之间和每个节点附近的分散。与之前研究的尺寸 $d<3$ 的模型相比，这里考虑的模型展示了 Thouless 电导的临界缩放，这允许{准确}确定非安德森跃迁的临界特性，其精度大大超过了从状态密度的临界缩放获得的结果，通常在这种转变中模拟。我们发现在消失参数 $\varepsilon=2\alpha-1$ 的极限下，相关长度指数 $\nu=2/(3|\varepsilon|)$ 与预测 $\nu_ 不一致{RG}=1/|\varepsilon|$ 扰动重整化组分析。我们的结果允许对非安德森无序驱动转变的 $\varepsilon$-expansions 的收敛性进行数值验证，并且一般来说，临界尺寸附近的相互作用场理论。我们发现在消失参数 $\varepsilon=2\alpha-1$ 的极限下，相关长度指数 $\nu=2/(3|\varepsilon|)$ 与预测 $\nu_ 不一致{RG}=1/|\varepsilon|$ 扰动重整化组分析。我们的结果允许对非安德森无序驱动转变的 $\varepsilon$-expansions 的收敛性进行数值验证，并且一般来说，临界尺寸附近的相互作用场理论。我们发现在消失参数 $\varepsilon=2\alpha-1$ 的极限下，相关长度指数 $\nu=2/(3|\varepsilon|)$ 与预测 $\nu_ 不一致{RG}=1/|\varepsilon|$ 扰动重整化组分析。我们的结果允许对非安德森无序驱动转变的 $\varepsilon$-expansions 的收敛性进行数值验证，并且一般来说，临界尺寸附近的相互作用场理论。