AKLT-like valence bond solid state in the frustrated ferromagnetic J₁-J₂ chain

Frustrated one-dimensional (1D) magnets are known as ideal playgrounds for new exotic quantum phenomena. We consider an elementary frustrated 1D system: the spin-1/2 ferromagnetic (J₁) Heisenberg chain with next-nearest-neighbor antiferromagnetic (AFM) (J₂) interactions. On the basis of density-matrix renormalization group calculations we show the existence of a finite spin gap at J₂/|J₁| > 1/4 and we find the ground state in this region to be a valence bond solid (VBS) with spin-singlet dimerization between third-neighbor sites. The VBS is the consequence of spontaneous symmetry breaking through order by disorder. Quite interestingly, this VBS state has a Affleck-Kennedy-Lieb-Tasaki-type topological order. We also investigate the possibility of multipolar physics induced by AFM interchain coupling.