Capturing correlation in the spin frustrated H-3-ring using the generator coordinate method and spin-constrained generalised Hartree-Fock states

In spin frustrated H-3-rings, variationally minimal single Slater determinant descriptions break (S) over cap (2) and (S) over cap (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.