Dedicated hardware for linearly-scaling algorithms in condensed-matter physics

The locality of the interactions in a Hamiltonian model gives origin to the linearization of the algorithms expressing the calculation of the interact ions. This specific property, often used in condensed matter physics, has o riginated approximate models which, although preserving most of the physica l insights of the parent exact models, display attractive computational pro perties which has determined their use in several scientific applications. We review the main issues at the basis of the linearization property arisin g in two different problems in condensed matter physics: the projection met hod to compute total energies in the Tight Binding approximation and the ca lculation of the pair-correlation function of weakly interacting bosons, in the Hypernetted-Chain expansion. We also remark how linearized numerical m odels 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 pu rposely design dedicated hardware devices which efficiently perform those n umerical calculations. (C) 2001 Elsevier Science B.V. All rights reserved.