Density-induced BCS to Bose-Einstein crossover

We investigate the zero-temperature BCS to Bose-Einstein crossover at the m ean-field level, by driving it with the attractive potential and the partic le density. We emphasize specifically the role played by the particle densi ty in this crossover. Three different interparticle potentials are consider ed for the continuum model in three spatial dimensions, while both s- and d -wave solutions are analyzed for the attractive (extended) Hubbard model on a two-dimensional square lattice. For this model the peculiar behavior of the crossover for the d-wave solution is discussed. In particular, in the s trung-coupling limit when approaching half-filling we evidence the occurren ce of strong correlations among antiparallel-spin fermions belonging to dif ferent composite bosons, which give rise to a quasi-long-range antiferromag netic order in this limit. [S0163-1829(99)00737-X].