Higgs criticality of Dirac spin liquids on depleted triangular lattices
Phys. Rev. B 114, 094411 – Published 7 August, 2026
DOI: https://doi.org/10.1103/nm1n-y5np
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 spin liquid, deriving the corresponding quantum electrodynamics -Higgs theory. While the triangular and kagome lattices share a low-energy description with Dirac fermions, the maple-leaf lattice yields an analogous theory with and a distinct nodal structure where the Dirac cones can move along high-symmetry lines in momentum space instead of gapping out. Using a large- expansion, we compute critical exponents and the scaling dimensions of the symmetry-allowed Yukawa couplings. Although Higgs-field fluctuations and a large fermion flavor number strongly suppress the Yukawa coupling—pushing the maple-leaf lattice closer to stability than its counterparts—we find that the coupling remains relevant at leading order in all three cases, substantially reducing its scaling dimension on the maple-leaf lattice and asymptotically breaking Lorentz and conformal invariance. Ultimately, our results provide a unified framework demonstrating how the interplay between fermion flavor count and nodal geometry dictates the fate of the -Higgs transition.