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

Abstract

We introduce a frustrated spin 1/2 Hamiltonian which is an extension of the two dimensional $J_1 - J_2$ Heisenberg model. The ground states of this model are exactly obtained at a first order quantum phase transition between two regions with different valence bond solid order parameters. At this point, the low energy excitations are deconfined spinons and spin-charge separation occurs under doping in the limit of low concentration of holes. In addition, this point is characterized by the proliferation of topological defects that signal the emergence of $Z_2$ gauge symmetry.