First order transition in the frustrated antiferromagnetic Heisenberg S=1 quantum spin chain

We study a frustrated Heisenberg S = 1 quantum spin chain with next-nearest neighbor (NNN) coupling alpha using a variational ansatz and the density matrix renormalization group. We find as quantum remnants of the phase transition in the classical chain a disorder point at alpha(D) = 0.284(1) and a Lifshitz point at alpha(L) = 0.3725(25). Our main finding is a first-order transition from an Affleck-Kennedy-Lieb-Tasaki (AKLT) phase to a NNN generalization of the AKLT phase at alpha(T) = 0.7443(6). At the transition, string order jumps discontinuously by approximate to 0.085 to 0; correlation length and gap are finite.