Comprehensive study of the phase diagram of the spin-12 Kitaev-Heisenberg-Gamma chain

Abstract

A central question on Kitaev materials is the effects of additional couplings on the Kitaev model, which is proposed to be a candidate for realizing topological quantum computations. However, two spatial dimensions typically suffer the difficulty of lacking controllable approaches. In this work, using a combination of powerful analytical and numerical methods available in one dimension, we perform a comprehensive study on the phase diagram of a one-dimensional version of the spin-1/2 Kitaev-Heisenberg-Gamma model in its full parameter space. A strikingly rich phase diagram is found with nine distinct phases, including four Luttinger liquid phases, a ferromagnetic phase, a Neél ordered phase, an ordered phase of distorted-spiral spin alignments, and two ordered phases, which both break a D3 symmetry albeit in different ways, where D3 is the dihedral group of order six. Our work paves the way for studying one-dimensional Kitaev materials and may provide hints to the physics in higher-dimensional situations.