arXiv subjects

Abee Nelson

Publications and source records attributed to Abee Nelson.

2 recordsLinked to original sources

arXiv2026

Quantum Criticality in Monolayer Amorphous Carbon

Amorphous solids represent the extreme limit of broken translational symmetry, in which the absence of long-range order removes well-defined crystal momenta and invalidates the Bloch description of electronic states. Monolayer amorphous carbon (MAC) has emerged as a unique realization of a strictly two-dimensional (2D) amorphous lattice defined by a structurally contiguous but topologically disordered $sp^2$-bonded random network devoid of any defined long-range crystal symmetry. From atomic-resolution measurements of multifractal wavefunctions, we show that disorder in MAC effectively localizes the low-energy part of the electronic spectrum but retains an extended critical-like state near the band centre ($E\sim 0$). We conjecture that this state is protected from topological disorder by remnant chiral symmetry surviving within the continuous random network, described by a Wess-Zumino-Witten (WZW) topological term. Near criticality, we verify the multifractal scaling relation $\eta = -\Delta_2$, providing quantitative agreement between independently measured spatial correlation decay and multifractal scaling exponents. Our results are confirmed by atomistic tight-binding calculations that closely mirror the multifractal scaling near $E\sim 0$. Our results establish MAC as the first strictly 2D amorphous electronic system to exhibit Anderson criticality driven purely by topological disorder

cond-mat.dis-nn↗

arXiv2023

Phase classification in the long-range Harper model using machine learning

In this work, we map the phase diagrams of one-dimensional quasiperiodic models using artificial neural networks. We observe that the multi-class classifier precisely distinguishes the various phases, namely the delocalized, multifractal, and localized phases, when trained on the eigenstates of the long-range Aubry-Andr\'e Harper (LRH) model. Additionally, when this trained multi-layer perceptron is fed with the eigenstates of the Aubry-Andr\'e Harper (AAH) model, it identifies various phases with reasonable accuracy. We examine the resulting phase diagrams produced using a single disorder realization and demonstrate that they are consistent with those obtained from the conventional method of fractal dimension analysis. Interestingly, when the neural network is trained using the eigenstates of the AAH model, the resulting phase diagrams for the LRH model are less exemplary than those previously obtained. Further, we study binary classification by training the neural network on the probability density corresponding to the delocalized and localized eigenstates of the AAH model. We are able to pinpoint the critical transition point by examining the metric ``accuracy" for the central eigenstate. The effectiveness of the binary classifier in identifying a previously unknown multifractal phase is then evaluated by applying it to the LRH model.

cond-mat.dis-nn↗