Exact ground states of a frustrated 2D magnet: Deconfined fractional excitations at a first-order quantum phase transition

A frustrated spin 1/2 Hamiltonian which is an extension of the two dimensional J₁-J₂ Heisenberg model was analyzed. The ground states of this model were obtained at a first-order quantum phase transition between two valence bond crystals (VBC). At this point, the low energy excitations were deconfined spinons and spin-charge separation was found to occur under doping in the limit of low concentration of holes. The analysis of the four chain model confirm that there are two VBC's separated by an approximately (1 + 1) Lorentz invariant quantum critical point.