Capturing correlation in the spin frustrated H₃-ring using the generator coordinate method and spin-constrained generalised Hartree-Fock states

In spin frustrated H3-rings, variationally minimal single Slater determinant descriptions break S^2 and S^z symmetries in an effort to simultaneously minimise the interactions between all electrons. Given the underlying spin dynamics, it remains unclear how one can move beyond these symmetry-broken mean-field states and efficiently introduce electron correlation. Here we show that in frustrated systems the average longitudinal magnetisation is a generator coordinate that is able to capture significant electron correlation. Our results demonstrate that tightly sampling the generator coordinate around spin phase transitions provides a good subspace for non-orthogonal configuration interaction. Combining these constrained generator coordinates with symmetry projection approaches could lead to efficient ansatzes that can incorporate complicated dynamics while maintaining symmetry quantum numbers.