Cristian D. Batista, Rolando D. Somma
One-dimensional quantum magnets can realize exotic states of matter such as Luttinger liquids, valence bond solids, and spin supersolids. A unique feature is that transmutations of particle statistics, that provide different representations of the same system, preserve the range of interactions. This is the main reason behind the success of spin-fermion transformations for studying one-dimensional spin systems. A simple generalization of such transformations maps spins into anyons, which are unusual particles that generalize the concept of fermions and bosons. By exploiting this generalization, we find the exact ground states of spin-1/2 frustrated magnets and provide an efficient method for computing correlation functions. These states are "anyon condensates" that spontaneously break the particle-number conservation symmetry. In contrast to the familiar Bose-Einstein condensates, the condensed particles satisfy anyonic statistics.
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http://arxiv.org/abs/1205.4946
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