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 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 $\epsilon =2\alpha -1$ the correlation-length exponent $\nu =2/(3|\epsilon |)$ at the transition is inconsistent with the prediction ${\nu }_{RG}=1/|\epsilon |$ 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.

12 pages

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Cited by in corpus (5)

• Rare regions and avoided quantum criticality in disordered Weyl semimetals and superconductors
• BCS-like disorder-driven instabilities and ultraviolet effects in nodal-line semimetals
• Direct topological insulator transitions in three dimensions are destabilized by non-perturbative effects of disorder
• Interactions-disorder duality and critical phenomena in nodal semimetals, dilute gases and other systems
• Information Bounds on phase transitions in disordered systems