q deformed formulation of Hamiltonian SU(3) Yang-Mills theory

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<jats:title>A<jats:sc>bstract</jats:sc> </jats:title><jats:p>We study SU(3) Yang-Mills theory in (2 + 1) dimensions based on networks of Wilson lines. With the help of the <jats:italic>q</jats:italic> deformation, networks respect the (discretized) SU(3) gauge symmetry as a quantum group, i.e., SU(3)<jats:sub><jats:italic>k</jats:italic></jats:sub>, and may enable implementations of SU(3) Yang-Mills theory in quantum and classical algorithms by referring to those of the stringnet model. As a demonstration, we perform a mean-field computation of the groundstate of SU(3)<jats:sub><jats:italic>k</jats:italic></jats:sub> Yang-Mills theory, which is in good agreement with the conventional Monte Carlo simulation by taking sufficiently large <jats:italic>k</jats:italic>. The variational ansatz of the mean-field computation can be represented by the tensor networks called infinite projected entangled pair states. The success of the mean-field computation indicates that the essential features of Yang-Mills theory are well described by tensor networks, so that they may be useful in numerical simulations of Yang-Mills theory.</jats:p>

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