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 dimension typically suffers 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 N\'eel ordered phase, an ordered phase of distorted-spiral spin alignments, and two ordered phase which both break a $D_3$ symmetry albeit in different ways, where $D_3$ 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.
Highlights
The Kitaev spin-1/2 model on the honeycomb lattice [1] with anisotropic bond-dependent Ising interactions is proposed to host exotic quasiparticle excitations, including Majorana fermions, and non-Abelian anyons under applied magnetic fields
Based on the classical analysis, we find that the “D3-breaking” region can be divided into two subregions corresponding to the “D3-breaking I” and the “D3-breaking invariant under H (II)” phases as shown in Fig. 1, which have Z(2I) and Z(2II) as the unbroken symmetry groups, respectively
We demonstrate that the firstorder projection of the perturbation term to the low-energy degrees of freedom remains to be of the XXZ type, indicating that there exists a region of Luttinger liquid which is stable against the perturbation
Summary
The Kitaev spin-1/2 model on the honeycomb lattice [1] with anisotropic bond-dependent Ising interactions is proposed to host exotic quasiparticle excitations, including Majorana fermions, and non-Abelian anyons under applied magnetic fields. We include a nonzero Heisenberg term, and make a comprehensive study of the phase diagram of the spin1/2 Kitaev-Heisenberg-Gamma chain in its full parameter space, using a combination of extensive analytical, DMRG and ED calculations. We have performed a careful symmetry analysis in each region to verify that the projected perturbation Hamiltonian contains all the symmetry allowed terms up to relevant and marginal couplings classified by the SU(2) critical theory In this way, five phases can be understood, including the Luttinger liquid phases “LL1,” “LL2,” and “LL3” (“LL” is “Luttinger liquid” for short), and the ordered phases “Néel” and “FM” with Néel and FM orders, respectively, which are all confirmed by our ED and DMRG numerical calculations. IX, we briefly summarize the main results and open questions of the paper
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