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

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.