Hidden symmetries of the extended Kitaev-Heisenberg model: Implications for honeycomb lattice iridates A2IrO3

TL;DR

This paper systematically uncovers hidden symmetries in a four-parameter spin model relevant to honeycomb iridates, revealing points of SU(2) symmetry that connect anisotropic models to the Heisenberg model, aiding in understanding experimental data.

Contribution

It introduces a general algorithm to identify dual transformations and hidden symmetries in bond-anisotropic spin models on various lattices, applied to honeycomb iridates.

Findings

Identified all hidden SU(2) symmetry points in the model.

Mapped anisotropic models to the Heisenberg model at symmetry points.

Provided parameter ranges consistent with experimental data for Na2IrO3 and Li2IrO3.

Abstract

We have explored the hidden symmetries of a generic four-parameter nearest-neighbor spin model, allowed in honeycomb lattice compounds under trigonal compression. Our method utilizes a systematic algorithm to identify all dual transformations of the model that map the Hamiltonian on itself, changing the parameters and providing exact links between different points in its parameter space. We have found the complete set of points of hidden SU(2) symmetry at which seemingly highly anisotropic model can be mapped back on the Heisenberg model and inherits therefore its properties such as the presence of gapless Goldstone modes. The procedure used to search for the hidden symmetries is quite general and may be extended to other bond-anisotropic spin models and other lattices, such as the triangular, kagome, hyper-honeycomb, or harmonic-honeycomb lattices. We apply our findings to the honeycomb lattice iridates Na2IrO3 and Li2IrO3, and illustrate how they help to identify plausible values of the model parameters that are compatible with the available experimental data.