Low-energy singlet and triplet excitations in the spin-liquid phase of the two-dimensionalJ1−J2model

We analyze the stability of the spontaneously dimerized phase of the frustrated Heisenberg antiferromagnet—the $J_1{-J}_2$ model—in two dimensions. The lowest triplet excitation, corresponding to breaking of a singlet bond, is found to be stable in the region $0.38\lesssim J_2{/J}_1\lesssim \mathrm{0.62.}$ In addition we find a stable low-energy collective singlet mode, which reflects the spontaneous violation of the discrete symmetry. The spontaneous dimerization vanishes at the point of second-order quantum transition into the Néel ordered phase $\left[{(J}_2{/J}_1{)}_{c1\mathrm{}}\approx 0.38\right].$ We argue that the disappearance of dimer order is related to the vanishing of the singlet energy gap at the transition point.