Spin-liquid phase for the frustrated quantum Heisenberg antiferromagnet on a square lattice

The existence of a spin-disordered ground state for the frustrated ${\mathit{J}}_{1\mathrm{-}}$ ${\mathit{J}}_{2\mathrm{-}}$ ${\mathit{J}}_3$ quantum Heisenberg antiferromagnet on a square lattice is reconsidered. It is argued that there is a unique action that is continuous through the whole phase diagram, except at the Lifshitz point, so that the Néel and helicoidal states cannot coexist and that there has to be an intermediate spin-liquid state. To show it, a detailed study combining spin-wave theory, Schwinger-boson mean-field theory, and a scaling analysis of the appropriate hydrodynamic action is performed. When done carefully, all these theories agree and strongly support the existence of the spin-liquid state.