  One approach for solving interacting many-fermion systems is the
configuration-interaction method, also sometimes called the interacting shell
model, where one finds eigenvalues of the Hamiltonian in a many-body basis of
Slater determinants (antisymmeterized products of single-particle
wavefunctions). The resulting Hamiltonian matrix is typically very sparse, but
for large systems the nonzero matrix elements can nonetheless require terabytes
or more of storage. An alternate algorithm, applicable to a broad class of
systems with symmetry, in our case rotational invariance, is to exactly
factorize both the basis and the interaction using additive/multiplicative
quantum numbers; such an algorithm can reduce the storage requirements by an
order of magnitude or more. We discuss factorization in general as well as in
the context of a specific configuration-interaction code, BIGSTICK, which runs
both on serial and parallel machines.
