Abstract
We propose a scheme to improve the coupled cluster expansion in lattice gauge theory (LGT), based on the application of the random phase approximation, in order to approximate a wave function in terms of a linear combination of Wilson loops. Using this method, we study the vacuum energy and vacuum wave function in $(2+1)\mathrm{D}$ SU(3) LGT up to fourth order. The vacuum energy is lower than that obtained by the unimproved approach. The coefficients ${\ensuremath{\mu}}_{0},{\ensuremath{\mu}}_{2}$ of the vacuum wave function show good scaling behavior and convergence.
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