Higgs criticality of Dirac spin liquids on depleted triangular lattices

TL;DR

This paper studies Higgs criticality in U(1) Dirac spin liquids on various depleted triangular lattices, analyzing how fermion flavor number and nodal structure influence the stability of the Higgs transition.

Contribution

It derives a unified theoretical framework connecting fermion flavor, nodal geometry, and the stability of the QED$_3$-Higgs transition in different lattice geometries.

Findings

Higgs-field fluctuations and large fermion flavor suppress Yukawa coupling relevance.

The maple-leaf lattice with more Dirac cones is closer to stability than triangular and kagome lattices.

Yukawa coupling remains weakly relevant, making the Higgs critical point asymptotically unstable.

Abstract

We investigate Higgs criticality in candidate U(1) Dirac spin liquids across a family of depleted triangular lattices: the triangular, kagome, and maple-leaf geometries. For each, we identify the symmetry-allowed spinon-pairing channel connecting the U(1) state to a proximate $\mathbb{Z}_2$ spin liquid, deriving the corresponding quantum electrodynamics (QED$_3$)-Higgs theory. While the triangular and kagome lattices share a low-energy description with $N_f=4$ Dirac fermions, the maple-leaf lattice yields an analogous theory with $N_f=12$ and a distinct nodal structure where the Dirac cones can move along high-symmetry lines in momentum space. Using a large-$N_{f,b}$ expansion, we compute critical exponents and the scaling dimensions of the symmetry-allowed Yukawa couplings. We find that while Higgs-field fluctuations and a large fermion flavor number both act to suppress the relevance of the Yukawa coupling -- pushing the maple-leaf lattice closer to stability than its counterparts -- the coupling remains weakly relevant in all three cases. This rendering of the Higgs critical point as asymptotically unstable is partly driven in the maple-leaf case by an additional coupling associated with the momentum-space mobility of the Dirac cones. Ultimately, our results provide a unified framework demonstrating how the interplay between fermion flavor count and nodal geometry dictates the fate of the QED$_3$-Higgs transition.