We introduce a general and accurate method for determining lattice phase shifts and mixing angles, which is applicable to arbitrary, non-cubic lattices. Our method combines angular momentum projection, spherical wall boundaries and an adjustable auxi
liary potential. This allows us to construct radial lattice wave functions and to determine phase shifts at arbitrary energies. For coupled partial waves, we use a complex-valued auxiliary potential that breaks time-reversal invariance. We benchmark our method using a system of two spin-1/2 particles interacting through a finite-range potential with a strong tensor component. We are able to extract phase shifts and mixing angles for all angular momenta and energies, with precision greater than that of extant methods. We discuss a wide range of applications from nuclear lattice simulations to optical lattice experiments.
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 $aleq 1.7$ fm, and we expect similar improvement for actual lattice Monte Carlo calculations.
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 usi
ng 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.
