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

Abstract

We study the breaking of rotational symmetry on the lattice for irreducible tensor operators and practical methods for suppressing this breaking. We illustrate the features of the general problem using an $\alpha$ cluster model for ${}^8$Be. We focus on the lowest states with non-zero angular momentum and examine the matrix elements of multipole moment operators. We show that the physical reduced matrix element is well reproduced by averaging over all possible orientations of the quantum state, and this is expressed as a sum of matrix elements weighted by the corresponding Clebsch-Gordan coefficients. For our $\alpha$ cluster model we find that the effects of rotational symmetry breaking can be largely eliminated for lattice spacings of $a\le 1.7$ fm, and we expect similar improvement for actual lattice Monte Carlo calculations.

8 pages, 4 figures

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Cited by in corpus (9)

• Microscopic Clustering in Light Nuclei
• Ab initio alpha-alpha scattering
• The long and winding road from chiral effective Lagrangians to nuclear structure
• Scattering cluster wave functions on the lattice using the adiabatic projection method
• Breaking and restoration of rotational symmetry in the low-energy spectrum of light alpha-conjugate nuclei on the lattice I: ${}^8\mathrm{Be}$ and ${}^{12}\mathrm{C}$
• P-Wave Two-Particle Bound and Scattering States in a Finite Volume including QED
• Magnetic dipole moments as a strong signature for $\alpha$-clustering in even-even self-conjugate nuclei
• Charge-dependent nucleon-nucleon interaction at N${}^3$LO in nuclear lattice effective field theory
• Clustering in nuclei from ab initio nuclear lattice simulations