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

TL;DR

This paper demonstrates that higher-level SU(2) Wess-Zumino-Witten models can be realized in spin chains with specific three-site interactions, confirmed through numerical simulations matching theoretical predictions.

Contribution

It shows that SU(2)_{k>1} Wess-Zumino-Witten models can be realized in spin chains with three-site interactions, extending previous understanding.

Findings

Numerical results match Wess-Zumino-Witten predictions for central charge and critical exponents.

Dimerization transition characterized for spins 1, 3/2, and 2.

Three-site interactions naturally induce the conditions for these models.

Abstract

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 (S_{i-1} S_i)(S_i S_{i+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 \eta=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.