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

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 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.

5 pages, 5 figures

References in corpus (2)

• The density-matrix renormalization group in the age of matrix product states
• DMRG studies of critical SU(N) spin chains

Cited by in corpus (11)

• Spontaneous dimerization, critical lines, and short-range correlations in a frustrated spin-1 chain
• From SU(2)${}_5$ to SU(2)${}_3$ Wess-Zumino-Witten transitions in a frustrated spin-5/2 chain
• Phase diagram of the alternating-spin Heisenberg chain with extra isotropic three-body exchange interactions
• Network construction of non-Abelian chiral spin liquids
• Chiral fixed point in a junction of critical spin-1 chains
• Phase diagram study of a dimerized spin-S zig-zag ladder
• Realization of Wess-Zumino-Witten transitions with levels $k=6$ and $k=4$ in a frustrated spin-3 chain
• Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids
• Haldane phases and phase diagrams of the S = 3/2, 1 bilinear-biquadratic Heisenberg model on the orthogonal dimer chain
• Heisenberg spin chains with additional isotropic three-site exchange interactions
• Confinement, deconfinement, and bound states in the spin-$1$ and spin-$3/2$ generalizations of the Majumdar--Ghosh chain