Interaction-driven competing instabilities in two-dimensional checkerboard quadratic band crossing semimetals
Abstract
Two-dimensional quadratic band crossing point (QBCP) semimetals serve as a fertile platform for interaction-driven quantum criticality, nevertheless, the role of the complete fermion-fermion interactions remains largely unexplored. To address this, we systematically investigate the low-energy physics of a spin-1/2 checkerboard-lattice QBCP semimetal by considering all 16 marginally short-range fermion-fermion interactions. Using the momentum-shell renormalization group, we derive the coupled flow equations, which reveal that the low-energy physics is governed by a series of fixed points. Depending on the initial conditions, the system may exhibit a single stable fixed point, several discrete fixed points, or three continuous groups of fixed points parameterized by a few variables. By introducing source terms and evaluating susceptibilities, we identify the dominant and subdominant instabilities. The leading phases include nematic spin-nematic (NSN), quantum anomalous Hall (QAH), chiral superconducting (SC1), and quantum spin Hall (QSH) orders. Moreover, several features distinguish our findings from previous simplified models. Off-diagonal interactions generate terms that promote orders absent in such models, the continuous groups allow systematic tuning of the leading instability, and trajectory-dependent instabilities emerge where the full RG flow, rather than the fixed point alone, determines the dominant state. These results offer a comprehensive theoretical understanding of low-energy quantum critical behaviors and phase instabilities in two-dimensional QBCP semimetals and related electron systems.
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BibTeX
@misc{wen2026interactiondriven,
title = {{Interaction-driven competing instabilities in two-dimensional checkerboard quadratic band crossing semimetals}},
author = {Jia-Hao Wen and Wen-Hao Bian and Jing Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25046},
eprint = {2610.25046},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25046},
}
RIS
TY - UNPB
TI - Interaction-driven competing instabilities in two-dimensional checkerboard quadratic band crossing semimetals
AU - Jia-Hao Wen
AU - Wen-Hao Bian
AU - Jing Wang
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25046
UR - https://arxiv.org/abs/2610.25046
AB - Two-dimensional quadratic band crossing point (QBCP) semimetals serve as a fertile platform for interaction-driven quantum criticality, nevertheless, the role of the complete fermion-fermion interactions remains largely unexplored. To address this, we systematically investigate the low-energy physics of a spin-1/2 checkerboard-lattice QBCP semimetal by considering all 16 marginally short-range fermion-fermion interactions. Using the momentum-shell renormalization group, we derive the coupled flow equations, which reveal that the low-energy physics is governed by a series of fixed points. Depending on the initial conditions, the system may exhibit a single stable fixed point, several discrete fixed points, or three continuous groups of fixed points parameterized by a few variables. By introducing source terms and evaluating susceptibilities, we identify the dominant and subdominant instabilities. The leading phases include nematic spin-nematic (NSN), quantum anomalous Hall (QAH), chiral superconducting (SC_1), and quantum spin Hall (QSH) orders. Moreover, several features distinguish our findings from previous simplified models. Off-diagonal interactions generate terms that promote orders absent in such models, the continuous groups allow systematic tuning of the leading instability, and trajectory-dependent instabilities emerge where the full RG flow, rather than the fixed point alone, determines the dominant state. These results offer a comprehensive theoretical understanding of low-energy quantum critical behaviors and phase instabilities in two-dimensional QBCP semimetals and related electron systems.
ER -