The seniority quantum number is the number of unpaired fermions in a many-body wavefunction. While it is not a new concept—it’s prehistory dates back at least to the 1950s—it is only relatively recently that seniority-based approaches to the quantum many-body problem have been systematically explored. The intrigue of seniority-based methods arises because the seniority-zero configuration interaction (sen0-CI), which is the exact wavefunction in the seniority-zero subspace, is a size-consistent selected CI method and often (but not always) captures strong electron correlation. Remarkably, sen0-CI can often be approximated very accurately by low-cost wavefunctions. We will show that this is not that surprising: every seniority-zero state can be written as a (number-symmetry-broken-and-projected) product of quasiparticles. (This result extends, albeit in an impractical way, to arbitrary-seniority states. It extends, in a more practical way, to bosons.)

While treating seniority-zero states is often computationally facile, most real systems do not preserve the seniority quantum number. We show how to map real Hamiltonians to seniority-zero Hamiltonians (which are then easy to treat). The inverse mapping effectively treats the residual correlation from a seniority-zero description.