Breaking and restoration of rotational symmetry for irreducible tensor operators on the lattice

We study the breaking of rotational symmetry on the lattice for irreducible tensor operators and practical methods for suppressing such breaking. We illustrate the features of the general problem using an a cluster model for Be-8. We focus on the lowest states with nonzero angular momentum and examine the matrix elements of multipole moment operators. We show that reduced matrix elements are well reproduced by averaging over all possible orientations of the quantum state. This averaging is performed in terms of a sum of matrix elements weighted by the Clebsch-Gordan coefficients of each orientation. For our alpha cluster model, we find that the effects of rotational symmetry breaking can be largely eliminated for lattice spacings of alpha <= 1.7 fm, and we expect similar improvement for lattice Monte Carlo calculations.