Scaling dimension of $4π$-flux monopole operator in four-flavor three-dimensional QED using lattice simulation
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| Format: | Preprint |
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2024
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| _version_ | 1866929205699149824 |
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| author | Karthik, Nikhil Narayanan, Rajamani |
| author_facet | Karthik, Nikhil Narayanan, Rajamani |
| contents | 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 $2π$ and $4π$ fluxes around them. We first show that the estimates for the monopole scaling dimensions are consistent with the large-$N$ expectations for $N=12$ QED$_3$. Applying the same procedure in $N=4$ QED$_3$, 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_01856 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Scaling dimension of $4π$-flux monopole operator in four-flavor three-dimensional QED using lattice simulation Karthik, Nikhil Narayanan, Rajamani High Energy Physics - Lattice Strongly Correlated Electrons High Energy Physics - Theory 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 $2π$ and $4π$ fluxes around them. We first show that the estimates for the monopole scaling dimensions are consistent with the large-$N$ expectations for $N=12$ QED$_3$. Applying the same procedure in $N=4$ QED$_3$, 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. |
| title | Scaling dimension of $4π$-flux monopole operator in four-flavor three-dimensional QED using lattice simulation |
| topic | High Energy Physics - Lattice Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2401.01856 |