Quantum-Geometric Amplification of Nonperturbative Interaction Scales
Abstract
Weak interactions at a two-dimensional quadratic band touching (QBT) can generate an exponentially small symmetry-breaking gap, m∼ e−A/V1, that cannot be captured by every finite order of perturbation theory. We show that the singular quantum geometry of the gapped QBT converts this beyond-all-orders scale into an algebraically enhanced response. The quantum metric develops a momentum-space hot spot whose Brillouin-zone integral diverges logarithmically, and therefore grows algebraically when the gap is dynamically generated by interactions. Through the inverse-frequency Souza--Wilkens--Martin optical sum rule, the same amplification appears in the negative-first longitudinal optical moment, even though the ordinary optical conductivity remains O(e2/ℏ) and its absorption threshold is exponentially small. We establish these results analytically for a massive QBT and verify them microscopically in an interacting kagome lattice model known to develop a spontaneous quantum anomalous Hall mass at its QBT from loop currents order. Our results identify quantum geometry as an asymptotic amplifier of nonperturbative interaction scales.
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BibTeX
@misc{bilamour2026quantumgeometric,
title = {{Quantum-Geometric Amplification of Nonperturbative Interaction Scales}},
author = {Stefano Bilamour and René Meyer and Johanna Erdmenger and Domenico Di Sante},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34607},
eprint = {2609.34607},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34607},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum-Geometric Amplification of Nonperturbative Interaction Scales
AU - Stefano Bilamour
AU - René Meyer
AU - Johanna Erdmenger
AU - Domenico Di Sante
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34607
UR - https://arxiv.org/abs/2609.34607
AB - Weak interactions at a two-dimensional quadratic band touching (QBT) can generate an exponentially small symmetry-breaking gap, m∼ e^−A/V_1, that cannot be captured by every finite order of perturbation theory. We show that the singular quantum geometry of the gapped QBT converts this beyond-all-orders scale into an algebraically enhanced response. The quantum metric develops a momentum-space hot spot whose Brillouin-zone integral diverges logarithmically, and therefore grows algebraically when the gap is dynamically generated by interactions. Through the inverse-frequency Souza--Wilkens--Martin optical sum rule, the same amplification appears in the negative-first longitudinal optical moment, even though the ordinary optical conductivity remains O(e^2/ℏ) and its absorption threshold is exponentially small. We establish these results analytically for a massive QBT and verify them microscopically in an interacting kagome lattice model known to develop a spontaneous quantum anomalous Hall mass at its QBT from loop currents order. Our results identify quantum geometry as an asymptotic amplifier of nonperturbative interaction scales.
ER -