Breaking and restoration of rotational symmetry on the lattice for bound state multiplets

Abstract

We explore the breaking of rotational symmetry on the lattice for bound state energies and practical methods for suppressing this breaking. We demonstrate the general problems associated with lattice discretization errors and finite-volume errors using an $\alpha$ cluster model for ${}^8$Be and ${}^{12}$C. We consider the two and three $\alpha$-particle systems and focus on the lowest states with non-zero angular momentum which split into multiplets corresponding to different irreducible representations of the cubic group. We examine the dependence of such splittings on the lattice spacing and box size. We find that lattice spacing errors are closely related to the commensurability of the lattice with the intrinsic length scales of the system. We also show that rotational symmetry breaking effects can be significantly reduced by using improved lattice actions, and that the physical energy levels are accurately reproduced by the weighted average of a given spin multiplets.

8 pages, 8 figures, 2 tables

References in corpus (7)

• Structure and rotations of the Hoyle state
• Toward the excited meson spectrum of dynamical QCD
• Nuclear Physics from Lattice QCD
• Scalar mesons in a finite volume
• Lattice Simulations for Light Nuclei: Chiral Effective Field Theory at Leading Order
• The triton in a finite volume
• Two- and three-alpha systems with nonlocal potential

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• Chiral Effective Field Theory after Thirty Years: Nuclear Lattice Simulations