Faster neighbour list generation using a novel lattice vector representation

In any many-body simulation where particles are coupled using short-range potentials, a key part of the simulation is to find which particles {j} interact with particle i. The set of such particles is known as the neighbour list of particle i. A novel algorithm is developed here which efficiently returns a neighbour list. A partially occupied reference lattice may be constructed for any simulation, with the position of particles defined as being a short vector separation from a node. A lattice vector which preserves translational symmetry in a periodic supercell under addition and subtraction operations can then be constructed from a single 32-bit integer number. A novel neighbour list algorithm is then developed which uses a single set of lattice vectors to return all nodes, and therefore all particles associated with the nodes, within a fixed radius sphere of particle i. This new algorithm preserves translational symmetry in a periodic supercell, requires a small memory overhead, and is shown to be faster than the well-known Linked-Cell method in all cases considered here.