Fermionic valence-bond approach in terms of SU(4) representation is proposed to describe the $J_1-J_2$ frustrated Heisenberg antiferromagnetic (AF) model on a bipartite square lattice. A uniform mean field solution without breaking the translational and rotational symmetries describes a valence-bond spin-liquid state, interpolating the two different AF ordered states in the large $J_1$ and large $J_2$ limits, respectively. This novel spin-liquid state is gapless with the vanishing density of states at the Fermi nodal points. Moreover, a sharp resonance peak in the dynamic structure factor is predicted for momenta $\mathbf{q}=(0,0)$ and $(\pi ,\pi )$ in the strongly frustrated limit $J_2/J_1\sim 1/2$, which can be checked by neutron scattering experiments.

• Received 24 March 2003

DOI:https://doi.org/10.1103/PhysRevLett.91.067201