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We study the ground-state phase diagram of a spin-1/2 XXZ model with achirality-chirality interaction (CCI) on a two-leg ladder. This model offers aminimal setup to study an interplay between spin and chirality degrees offreedom. The spin-chirality duality transformation allows us to relate theregimes of weak and strong CCIs. By applying the Abelian bosonization and theduality, we obtain a rich phase diagram that contains distinct gappedfeatureless and ordered phases. In particular, Neel and vector chiral ordersappear for easy-axis anisotropy, while two distinct symmetry protectedtopological (SPT) phases appear for easy-plane anisotropy. The two SPT phasescan be viewed as twisted variants of the Haldane phase. We also present aneffective description in terms of (spinor) hard-core bosons, which revealscritical behavior on the self-dual line in the easy-axis and easy-planeregimes. We perform numerical simulations to confirm the predicted phasestructure and critical properties. We further demonstrate that the two SPTphases and a trivial phase are distinguished by topological indices in thepresence of certain symmetries. A similar phase structure is expected in aspin-1/2 XXZ ladder with four-spin ring exchange.

Symmetry, topology, duality, chirality, and criticality in a spin-1/2 XXZ ladder with a four-spin interaction