Comprehensive study of the phase diagram of the spin-1/2 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 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 Néel 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.

53 pages, 29 figures

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• Measurement-based quantum computation in finite one-dimensional systems: string order implies computational power
• Exact matrix product states at the quantum Lifshitz tricritical point in a spin-1/2 zigzag-chain antiferromagnet with anisotropic $\Gamma$-term
• Insights into the Anisotropic Spin-$S$ Kitaev Chain
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• Spin wave theory of one-dimensional generalized Kitaev model
• Symmetry analysis of bond-alternating Kitaev spin chains and ladders
• State selection in frustrated magnets
• Information propagation in one-dimensional XY-$\Gamma$ chains
• Spontaneous dimerization, spin-nematic order, and deconfined quantum critical point in a spin-1 Kitaev chain with tunable single-ion anisotropy
• Origin of nonsymmorphic bosonization formulas in generalized antiferromagnetic Kitaev spin-$\frac{1}{2}$ chains from a renormalization-group perspective
• Static magnetic and ESR spectroscopic properties of the dimer-chain antiferromagnet BiCoPO${}_5$
• Extended Quantum Spin Liquid with Spinon-like Excitations in an Anisotropic Kitaev-Gamma Model
• Cobalt-Based Pyroxenes: A New Playground for Kitaev Physics and Ising Model Realization
• Nonsymmorphic bosonization in one-dimensional generalized Kitaev spin-1/2 models
• Emergent SU(2)${}_1$ conformal symmetry in the spin-1/2 Kitaev-Gamma chain with a Dzyaloshinskii-Moriya interaction
• Left-left-right-right magnetic order in spin-1/2 Kitaev-Heisenberg chain
• Continuous phase transition from a chiral spin state to collinear magnetic order in a zigzag chain with Kitaev interactions
• Nonsymmorphic spin-space cubic groups and SU(2)${}_1$ conformal invariance in one-dimensional spin-1/2 models
• Assembling Kitaev honeycomb spin liquids from arrays of 1D symmetry protected topological phases
• Ground-state phase diagram of anisotropically interacting Heisenberg-$\Gamma$ models on a honeycomb lattice
• Finite-Size Spectral Signatures of Order by Quantum Disorder: A Perspective from Anderson's Tower of States