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

• URL: http://arxiv.org/abs/2306.12324v2
• Date: Tue, 19 Sep 2023 05:43:45 GMT
• Title: $q$ deformed formulation of Hamiltonian SU(3) Yang-Mills theory
• Authors: Tomoya Hayata, Yoshimasa Hidaka
• Abstract summary: We study $mathrmSU(3)$ Yang-Mills theory in $ (2+1)$ dimensions based on networks of Wilson lines. We perform a mean-field computation of the groundstate of $mathrmSU(3)_k$ Yang-Mills theory. The success of the mean-field computation indicates that the essential features of Yang-Mills theory are well described by tensor networks.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study $\mathrm{SU}(3)$ Yang-Mills theory in $(2+1)$ dimensions based on networks of Wilson lines. With the help of the $q$ deformation, networks respect the (discretized) $\mathrm{SU}(3)$ gauge symmetry as a quantum group, i.e., $\mathrm{SU}(3)_k$, and may enable implementations of $\mathrm{SU}(3)$ 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 $\mathrm{SU}(3)_k$ 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.

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