Scaling dimension of the 4π -flux monopole operator in four-flavor three-dimensional QED using lattice simulation

We numerically address the issue of which monopole operators are relevant under renormalization group flow in three-dimensional parity-invariant noncompact QED with four flavors of massless two-component Dirac fermion. Using lattice simulation and finite-size scaling analysis of the free energy to introduce monopole-antimonopole pairs in N=4 and N=12 flavor noncompact QED3, we estimate the infrared scaling dimensions of monopole operators that introduce 2π and 4π fluxes around them. We first show that the estimates for the monopole scaling dimensions are consistent with the large-N expectations for N=12 QED3. Applying the same procedure in N=4 QED3, we estimate the scaling dimension of 4π flux monopole operator to be 3.7(3), which allows the possibility of the operator being irrelevant. This finding offers support to the scenario in which higher-flux monopoles are irrelevant deformations to the Dirac spin liquid phase that could be realized on certain non-bipartite lattices by forbidding 2π-flux monopoles. Published by the American Physical Society 2024