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We theoretically study one-dimensional spin-1/2 multiferroic systems. We focus on the chiral ordered phase with gapless excitations that appears under easy-plane anisotropy. The in-plane chirality dynamics contains gapless solitons associated with local flips of the chirality. These excitations contribute to the low-frequency dielectric response through the magnetoelectric coupling.

We review the random loop representations of Tóth and Aizenman-Nachtergaele for quantum Heisenberg models. They can be combined and extended so as to include the quantum XY model and certain SU(2)-invariant spin 1 systems. We explain the calculations of correlation functions.