Scaling dimension of the 4 π flux monopole operator in fourflavor threedimensional QED using lattice simulation
Abstract
We numerically address the issue of which monopole operators are relevant under renormalization group flow in threedimensional parityinvariant noncompact QED with four flavors of massless twocomponent Dirac fermion. Using lattice simulation and finitesize scaling analysis of the free energy to introduce monopoleantimonopole pairs in N =4 and N =12 flavor noncompact QED_{3} , we estimate the infrared scaling dimensions of monopole operators that introduce 2 π and 4 π fluxes around them. We first show that the estimates for the monopole scaling dimensions are consistent with the largeN expectations for N =12 QED_{3} . Applying the same procedure in N =4 QED_{3} , we estimate the scaling dimension of 4 π 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 higherflux monopoles are irrelevant deformations to the Dirac spin liquid phase that could be realized on certain nonbipartite lattices by forbidding 2 π flux monopoles.
 Publication:

Physical Review D
 Pub Date:
 February 2024
 DOI:
 10.1103/PhysRevD.109.034507
 arXiv:
 arXiv:2401.01856
 Bibcode:
 2024PhRvD.109c4507K
 Keywords:

 High Energy Physics  Lattice;
 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Theory
 EPrint:
 12 pages, 9 figures