Haldane and dimer phases in a frustrated spin chain: an exact groundstate and associated topological phase transition

Abstract

A Heisenberg spin-s chain with alternating ferromagnetic (FM) () and antiferromagnetic () nearest-neighbor (NN) interactions, exhibits the dimer and spin-2s Haldane phases in the limits and respectively. These two phases are understood to be topologically equivalent. Induction of the frustration through the next NN FM interaction () produces a very rich quantum phase diagram. With frustration, the whole phase diagram is divided into a FM and a nonmagnetic (NM) phase. For s = 1/2, the full NM phase is seen to be of Haldane–dimer type, but for s > 1/2, a spiral phase comes between the FM and the Haldane–dimer phases. The study of a suitably defined string-order parameter and spin-gap at the phase boundary indicates that the Haldane–dimer and spiral phases have different topological characters. We also find that, along the line in the NM phase, an NN dimer state is the exact groundstate, provided where κ ⩽ s + h for applied magnetic field h. Without magnetic field, the position of JC is on the FM–NM phase boundary when s = 1/2, but for s > 1/2, the location of JC is on the phase separation line between the Haldane–dimer and spiral phases.