Condensation of Anyons in Frustrated Quantum Magnets

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We derive the exact ground space of a family of spin-1/2 Heisenberg chains with uniaxial exchange anisotropy (XXZ) and interactions between nearest and next-nearest-neighbor spins. The Hamiltonian family, H(Q), is parametrized by a single variable Q. By using a generalized Jordan-Wigner transformation that maps spins into anyons, we show that the exact ground states of H(Q) correspond to a condensation of anyons with statistical phase phi=-4Q. We also provide matrix-product state representations of some ground states that allow for the efficient computation of spin-spin correlation functions.