Realization of higher Wess-Zumino-Witten models in spin chains

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Building on the generalization of the exactly dimerized Majumdar-Ghosh ground state to arbitrary spin S for the Heisenberg chain with a three-site term (Sᵢ₋₁ Sᵢ)(Sᵢ Sᵢ₊₁) + H.c., we use density-matrix renormalization group simulations and exact diagonalizations to determine the nature of the dimerization transition for S=1, 3/2 and 2. The resulting central charge and critical exponent are in good agreement with the SU(2)ₖ₌₂ₛ Wess-Zumino-Witten values c=3k/(2+k) and η=3/(2+k). Since the 3-site term that induces dimerization appears naturally if exchange interactions are calculated beyond second order, these results suggest that SU(2)ₖ>₁ Wess-Zumino-Witten models might finally be realized in actual spin chains.