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arXiv · 2504.11523

Instability of the critical Ngai's coupling and two-boson mechanism in metals

Phu Nguyen·Vladyslav Kozii
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Abstract

We study the properties of a Fermi liquid coupled to a quantum critical boson via the two-boson interaction known as Ngai's coupling. We find that the original quantum critical point is generally unstable, resulting in a finite-momentum spatially modulated state unless two conditions are satisfied: (i) the critical boson is polar and transverse, and (ii) the ratio of the Fermi velocity to the transverse-boson velocity is sufficiently large. If these conditions hold and the uniform state remains stable, we demonstrate that the system enters a strong-coupling regime below a certain energy scale. In this regime, we discuss a self-consistent solution at criticality in two-dimensional systems and show that the critical boson field develops a nontrivial anomalous dimension, $\eta=1/2$. Our findings highlight the significant role of two-boson coupling in critical theories, challenging the conventional view that its effects are subdominant to linear coupling.

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Phu Nguyen, Vladyslav Kozii. 2025-04-15. Instability of the critical Ngai's coupling and two-boson mechanism in metals. https://arxiv.org/abs/2504.11523

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