Dedicated hardware for linearly-scaling algorithms in condensed-matter physics Original Research Article

The locality of the interactions in a Hamiltonian model gives origin to the linearization of the algorithms expressing the calculation of the interactions. This specific property, often used in condensed matter physics, has originated approximate models which, although preserving most of the physical insights of the parent exact models, display attractive computational properties which has determined their use in several scientific applications. We review the main issues at the basis of the linearization property arising in two different problems in condensed matter physics: the projection method to compute total energies in the Tight Binding approximation and the calculation of the pair-correlation function of weakly interacting bosons, in the Hypernetted-Chain expansion. We also remark how linearized numerical models could be mapped into “Systems of Affine Recurrence Equations” (SARE). The SARE structures revealed to be tractable with recently developed tools for hardware/software automatic synthesis. These tools could be used to purposely design dedicated hardware devices which efficiently perform those numerical calculations.