Modeling strong correlation is so difficult that theorists often settle for qualitative descriptions of strongly-correlated substances (e.g. heavy-fermion materials, high-temperature superconductors). These qualitative approaches are typically based on model Hamiltonians for which the Schrödinger equation can be solved exactly via the Bethe ansatz. In this way one ensures that at least the key qualitative features of the system are all captured. We recently realized that wavefunction forms inspired by algebraic models could also be used to obtain quantitative accuracy, while maintaining the computational feasibility associated with the simplified model systems.