Ground state and low-energy excitations of the Kitaev-Heisenberg ladder

Abstract

We study the ground state and low-lying excited states of the Kitaev-Heisenberg model on a ladder geometry using the density matrix renormalization group and Lanczos exact diagonalization methods. The Kitaev and Heisenberg interactions are parametrized as $K=\sin \varphi$ and $J=\cos \varphi$ with an angle parameter $\varphi$. Based on the results for several types of order parameters, excitation gaps, and entanglement spectra, the $\varphi$-dependent ground-state phase diagram is determined. Remarkably, the phase diagram is quite similar to that of the Kitaev-Heisenberg model on a honeycomb lattice, exhibiting the same long-range ordered states, namely rung-singlet (analog to Néel in 3D), zigzag, ferromagnetic, and stripy; and the presence of Kitaev spin liquids around the exactly solvable Kitaev points $\varphi =\pm \pi /2$. We also calculate the expectation value of a plaquette operator corresponding to a $\pi$-flux state in order to establish how the Kitaev spin liquid extends away from the $\varphi =\pm \pi /2$. Furthermore, we determine the dynamical spin structure factor and discuss the effect of the Kitaev interaction on the spin-triplet dispersion.

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• Insights into the Anisotropic Spin-$S$ Kitaev Chain
• Spin dynamics of the generalized quantum spin compass chain
• Emergent glassiness in disorder-free Kitaev model: Density matrix renormalization group study on a one-dimensional ladder setting
• String and conventional order parameters in the solvable modulated quantum chain
• Symmetry analysis of bond-alternating Kitaev spin chains and ladders
• Spin wave theory of one-dimensional generalized Kitaev model
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• Origin of nonsymmorphic bosonization formulas in generalized antiferromagnetic Kitaev spin-$\frac{1}{2}$ chains from a renormalization-group perspective
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• Left-left-right-right magnetic order in spin-1/2 Kitaev-Heisenberg chain
• Nonsymmorphic bosonization in one-dimensional generalized Kitaev spin-1/2 models
• Symmetry, topology, duality, chirality, and criticality in a spin-1/2 XXZ ladder with a four-spin interaction
• Emergent Quadrupolar Order in the Spin-$1/2$ Kitaev-Heisenberg Model
• Nonsymmorphic spin-space cubic groups and SU(2)${}_1$ conformal invariance in one-dimensional spin-1/2 models
• Brane order and quantum magnetism in modulated anisotropic ladders
• Continuous phase transition from a chiral spin state to collinear magnetic order in a zigzag chain with Kitaev interactions
• Eleven Competing Phases in the Heisenberg-Gamma (J$\Gamma$) Ladder
• Reviving Majorana zero modes in the spin-1/2 Kitaev ladder model
• Magnetic plateaus and jumps in a spin-1/2 ladder with alternate Ising-Heisenberg rungs: a field dependent study
• Ground State Properties of the Doped Kitaev-Heisenberg Chain: Topological Superconducting and Mott Insulating Phases Driven by Magnetic Frustration