Q Deformed Formulation of Hamiltonian SU(3) Yang-Mills Theory

We study SU(3) Yang-Mills theory in (2+1) dimensions based on networks of Wilson lines. With the help of the q deformation, networks respect the (discretized) SU(3) gauge symmetry as a quantum group, i.e., SU(3)_k, 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)_k Yang-Mills theory, which is in good agreement with the conventional Monte Carlo simulation by taking sufficiently large k. 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.