Interacting Chern insulator transition on the sphere: revealing the Gross-Neveu-Yukawa criticality
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| Format: | Preprint |
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2025
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| _version_ | 1866908349000318976 |
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| author | Gao, Zhi-Qiang Wang, Taige Lee, Dung-Hai |
| author_facet | Gao, Zhi-Qiang Wang, Taige Lee, Dung-Hai |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_15338 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Interacting Chern insulator transition on the sphere: revealing the Gross-Neveu-Yukawa criticality Gao, Zhi-Qiang Wang, Taige Lee, Dung-Hai Strongly Correlated Electrons Mesoscale and Nanoscale Physics Statistical Mechanics High Energy Physics - Theory 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. |
| title | Interacting Chern insulator transition on the sphere: revealing the Gross-Neveu-Yukawa criticality |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2504.15338 |