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arXiv:cond-mat/9606007 · Physical review. B, Condensed matter

Non-Abelian bosonization of the frustrated antiferromagnetic spin-1/2 chain

Dave Allen, David Sénéchal

Published Jan 1, 1997• 90 citations
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Abstract

We study the spin-1/2 chain with nearest-neighbor (${\mathrm{\ensuremath{\kappa}}}_{1}$) and next-nearest-neighbor (${\mathrm{\ensuremath{\kappa}}}_{2}$) interactions in the regime ${\mathrm{\ensuremath{\kappa}}}_{2}$\ensuremath{\gg}:${\mathrm{\ensuremath{\kappa}}}_{1}$, which is equivalent to two chains with a ``zigzag'' interaction. In the continuum limit, this system is described in terms of two coupled level-1 Wess-Zumino-Witten field theories. We illustrate its equivalence with four off-critical Ising models (Majorana fermions). This description is used to investigate the opening of a gap as a function of ${\mathrm{\ensuremath{\kappa}}}_{1}$ and the associated spontaneous breakdown of parity. We calculate the dynamic spin structure factor near the wave vectors accessible to the continuum limit. We comment on the nonzero string order parameter and show the presence of a hidden ${\mathrm{Z}}_{2}$\ifmmode\times\else\texttimes\fi{}${\mathrm{Z}}_{2}$ symmetry via a nonlocal transformation on the microscopic Hamiltonian. For a ferromagnetic interchain coupling, the model is conjectured to be critical, with different velocities for the spin-singlet and spin-triplet excitations.

DOI
10.1103/physrevb.55.299

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We study dimerization transitions in a frustrated spin-3 chain with next-nearest-neighbor and three-site interactions. We show that two independent coupling constants of the model are sufficient to fine-tune the system to the critical point in the Wess-Zumino-Witten SU(2)6\mathrm{SU}{(2)}_{6}SU(2)6​ universality class. This critical point appears as the end point of an extended SU(2)4\mathrm{SU}{(2)}_{4}SU(2)4​ critical line. This implies that the renormalization group flow leads to the critical theory with the largest level kkk such that the number of relevant operators is reduced by one and the parity of the level is preserved. Furthermore, we argue that due to the presence of marginal operator there is only one point in the SU(2)6\mathrm{SU}{(2)}_{6}SU(2)6​ universality class. In addition, we report the appearance of the nonmagnetic Ising transition between the topologically trivial uniform and dimerized phases. This transition takes place within the singlet sector, while the magnetic gap remains open.
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