First Order Transition in the Frustrated Antiferromagnetic Heisenberg S=1 Quantum Spin Chain.

Abstract

We study a frustrated Heisenberg $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ quantum spin chain with next-nearest neighbor (NNN) coupling $\ensuremath{\alpha}$ 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 ${\ensuremath{\alpha}}_{D}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.284(1)$ and a Lifshitz point at ${\ensuremath{\alpha}}_{L}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.3725(25)$. 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 ${\ensuremath{\alpha}}_{T}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.7444(6)$. At the transition, string order jumps discontinuously by $\ensuremath{\approx}0.085$ to 0; correlation length and gap are finite.