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

TL;DR

This paper analyzes a frustrated spin-1/2 chain using non-Abelian bosonization, revealing a complex phase structure, gap formation, and hidden symmetries through a continuum field theory approach.

Contribution

It introduces a non-Abelian bosonization framework for the frustrated spin chain, connecting it to coupled WZW models and Ising models, and explores its phase transitions and symmetries.

Findings

Identification of a gap opening related to interaction parameters

Presence of a hidden ${Bbb Z}_2\times{\bBbb Z}_2$ symmetry

Conjecture of criticality with different excitation velocities

Abstract

We study the spin-1/2 chain with nearest neighbor ($\kappa_1$) and next-nearest neighbor ($\kappa_2$) interactions in the regime $\kappa_2\gg \kappa_1$, which is equivalent to two chains with a `zig-zag' interaction. In the continuum limit, this system is described in term of two coupled level-1 WZW 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 $\kappa_1$ and the associated spontaneous breakdown of parity. We calculate the dynamic spin structure factor near the wavevectors accessible to the continuum limit. We comment on the nonzero string order parameter and show the presence of a hidden ${\Bbb Z}_2\times{\Bbb Z}_2$ 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.