Spontaneous dimerization in the ground state of one-dimensional frustrated Heisenberg antiferromagnets

Starting from the exact result of Majumdar and Ghosh for the dimerized ground state of a Heisenberg linear-chain antiferromagnet with competing next-nearest-neighbor interaction J2=1/2J1, it is shown that this state is an exact eigenstate of the same Hamiltonian with couplings extended up to fourth-nearest neighbors, if the relations J1-2J2+J3=0 and J3=2J4 hold. Furthermore, it is proved to all orders in perturbation theory that this state is the ground state of this Hamiltonian in a finite interval of values of the parameter =1/2-j2 around =0. The actual extension of this interval is computed numerically for finite chains and is shown to be significant.