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arXiv · 2504.15338

Interacting Chern insulator transition on the sphere: revealing the Gross-Neveu-Yukawa criticality

Zhi-Qiang Gao·Taige Wang·Dung-Hai Lee
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Abstract

In two spatial dimensions, the transition between topological and trivial Chern insulators exemplifies a class of beyond-Landau critical phenomena. We show that the interaction-driven multicritical point of this transition falls into the Gross-Neveu-Yukawa (GNY) universality class, a topic of considerable interest in both high-energy and condensed matter physics. In this work, we focus on the $N=2$ case of the GNY criticality. We employ exact diagonalization of Dirac fermions on a sphere to circumvent the parity anomaly, capitalize on full $SO(3)$ symmetry to reduce finite-size effects, and directly extract operator scaling dimensions from the excitation spectrum. Despite working with only modest system sizes, our results closely match conformal bootstrap predictions for low-scaling dimension operators and reveal several previously uncharacterized higher primaries. These findings highlight the efficacy of spherical geometry for probing interacting Dirac criticality.

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Zhi-Qiang Gao, Taige Wang, Dung-Hai Lee. 2025-04-21. Interacting Chern insulator transition on the sphere: revealing the Gross-Neveu-Yukawa criticality. https://arxiv.org/abs/2504.15338

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