Phase diagram of the spin-1/2 Kitaev-Gamma chain and emergent SU(2) symmetry

TL;DR

This paper investigates a one-dimensional Kitaev-Gamma spin-1/2 chain, revealing an emergent SU(2) symmetry in the gapless phase and symmetry breaking in the ordered phase, using analytical and numerical methods.

Contribution

It uncovers an emergent SU(2) symmetry in the gapless phase and proposes a modified bosonization formula for the exotic partial symmetry.

Findings

Emergent SU(2)$_1$ WZW model describes low-energy physics.

Spin correlations show SU(2) breaking prefactors.

Evidence of $O_h ightarrow D_4$ symmetry breaking in ordered phase.

Abstract

We study the phase diagram of a one-dimensional version of the Kitaev spin-1/2 model with an extra ``$\Gamma$-term", using analytical, density matrix renormalization group and exact diagonalization methods. Two intriguing phases are found. In the gapless phase, although the exact symmetry group of the system is discrete, the low energy theory is described by an emergent SU(2)$_1$ Wess-Zumino-Witten (WZW) model. On the other hand, the spin-spin correlation functions exhibit SU(2) breaking prefactors, even though the exponents and the logarithmic corrections are consistent with the SU(2)$_1$ predictions. A modified nonabelian bosonization formula is proposed to capture such exotic emergent ``partial" SU(2) symmetry. In the ordered phase, there is numerical evidence for an $O_h\rightarrow D_4$ spontaneous symmetry breaking.