Symmetry-resolved monopoles and stability criteria for an Nf=12 Dirac spin liquid on the maple-leaf lattice
Abstract
The 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 operators of the compact gauge field can proliferate and confine the spinons. Here we determine the symmetry quantum numbers of the fundamental monopoles of a maple-leaf-lattice Dirac spin liquid whose generic six-node regime realizes QED3 with Nf=12 two-component Dirac fermions. The charge-one monopoles span a $924$-dimensional complex representation. In the spin-singlet, zero-momentum, zero-C6-angular-momentum sector we find five complex charge-one directions, of which three are mapped to their Hermitian conjugates under time reversal. Their real and imaginary Hermitian combinations therefore supply six independent monopole perturbations that are trivial under translations, C6, time reversal, and spin rotation. The Dirac spin liquid phase is thus not protected by symmetry exclusion of charge-one monopoles: its stability depends on whether these allowed perturbations are relevant in the renormalization group sense. Existing large-Nf and numerical estimates of the charge-one monopole scaling dimension lie close to the relevance threshold, making the maple-leaf lattice a concrete platform for testing the stability of compact QED3 in a quantum magnet. Our complete monopole classification also identifies the spin, momentum, and rotation sectors in which monopole excitations should appear, providing symmetry-resolved benchmarks for exact-diagonalization and variational tests of the Nf=12 Dirac spin liquid.
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BibTeX
@misc{zhang2026symmetryresolved,
title = {{Symmetry-resolved monopoles and stability criteria for an $N_f=12$ Dirac spin liquid on the maple-leaf lattice}},
author = {Yunchao Zhang and Andreas Feuerpfeil and Subir Sachdev and Ronny Thomale and Yasir Iqbal},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.21587},
eprint = {2605.21587},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.21587},
}
RIS
TY - UNPB
TI - Symmetry-resolved monopoles and stability criteria for an N_f=12 Dirac spin liquid on the maple-leaf lattice
AU - Yunchao Zhang
AU - Andreas Feuerpfeil
AU - Subir Sachdev
AU - Ronny Thomale
AU - Yasir Iqbal
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2605.21587
UR - https://arxiv.org/abs/2605.21587
AB - The 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 operators of the compact gauge field can proliferate and confine the spinons. Here we determine the symmetry quantum numbers of the fundamental monopoles of a maple-leaf-lattice Dirac spin liquid whose generic six-node regime realizes QED_3 with N_f=12 two-component Dirac fermions. The charge-one monopoles span a $924$-dimensional complex representation. In the spin-singlet, zero-momentum, zero-C_6-angular-momentum sector we find five complex charge-one directions, of which three are mapped to their Hermitian conjugates under time reversal. Their real and imaginary Hermitian combinations therefore supply six independent monopole perturbations that are trivial under translations, C_6, time reversal, and spin rotation. The Dirac spin liquid phase is thus not protected by symmetry exclusion of charge-one monopoles: its stability depends on whether these allowed perturbations are relevant in the renormalization group sense. Existing large-N_f and numerical estimates of the charge-one monopole scaling dimension lie close to the relevance threshold, making the maple-leaf lattice a concrete platform for testing the stability of compact QED_3 in a quantum magnet. Our complete monopole classification also identifies the spin, momentum, and rotation sectors in which monopole excitations should appear, providing symmetry-resolved benchmarks for exact-diagonalization and variational tests of the N_f=12 Dirac spin liquid.
ER -