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arXiv · 2401.01856

Scaling dimension of $4\pi$-flux monopole operator in four-flavor three-dimensional QED using lattice simulation

Nikhil Karthik·Rajamani Narayanan
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Abstract

We numerically address the issue of which monopole operators are relevant under renormalization group flow in three-dimensional parity-invariant noncompact QED with $4$ 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 QED$_3$, we estimate the infrared scaling dimensions of monopole operators that introduce $2\pi$ and $4\pi$ fluxes around them. We first show that the estimates for the monopole scaling dimensions are consistent with the large-$N$ expectations for $N=12$ QED$_3$. Applying the same procedure in $N=4$ QED$_3$, we estimate the scaling dimension of $4\pi$ 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 $2\pi$-flux monopoles.

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Nikhil Karthik, Rajamani Narayanan. 2024-01-03. Scaling dimension of $4\pi$-flux monopole operator in four-flavor three-dimensional QED using lattice simulation. https://arxiv.org/abs/2401.01856

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