Large-flavor route to a stable U(1) Dirac spin liquid on the maple-leaf lattice

Abstract

The $\mathrm{U}(1)$ Dirac spin liquid provides a useful organizing framework for frustrated magnets: it offers an algebraic parent state from which competing orders, confinement patterns, and low-energy spectral features can be understood. Whether such a state can occur as a stable ground state of a two-dimensional spin Hamiltonian remains an open question, because monopole events of the compact gauge field can proliferate and confine the spinons. Here, we show that the maple-leaf lattice provides a distinct route to this problem. Its Dirac spin liquid realizes QED$_3$ with $N_f=12$ Dirac fermions, substantially more than the $N_f=4$ theories of the triangular and kagome lattices. We classify the fundamental monopoles under the full microscopic symmetry group and find five charge-one spin-singlet monopoles that are trivial under lattice symmetries, time reversal, and spin rotation. The phase is therefore not protected by symmetry in the usual sense: its stability depends on whether these allowed monopoles are dynamically irrelevant. Available large-$N_f$ and Monte Carlo estimates place the charge-one monopole dimension close to the relevance threshold in $(2+1)$ dimensions, making the maple-leaf lattice a concrete large-flavor platform for testing the stability of compact QED$_3$ in a quantum magnet. The same monopole classification gives direct numerical predictions, identifying the symmetry sectors in which singlet, triplet, and quintet monopole excitations should appear. This provides a route to testing the $N_f=12$ Dirac spin liquid through symmetry-resolved exact diagonalization and variational studies of maple-leaf spin Hamiltonians.