Fig. 4: Distinct boundary magnon excitations for the [001] and [111] polarized FM orders.
From: Kinetic ferromagnetism and topological magnons of the hole-doped Kitaev spin liquid
![Fig. 4: Distinct boundary magnon excitations for the [001] and [111] polarized FM orders.](http://media.springernature.com/full/springer-static/image/art%3A10.1038%2Fs41535-024-00678-8/MediaObjects/41535_2024_678_Fig4_HTML.png?as=webp)
a Magnon bands on a cylinder for a [001] ordered state within nonlinear SWT. The real-time dynamics of (b) spin current js(t, x) and (c) charge current jc(x, t) for a [001] ordered state. These results are obtained by DMRG using one-hole doped YC3 cylinders (δ ≈ 0.013). For a–c, we set the off-diagonal exchange Γ = 0 and hopping strength t = 10K. The self-consistent solution with doping level δ = 0.01 gives kinetic hole energy \(\langle {\hat{P}}_{jk}\rangle \approx -0.93\times 1{0}^{-2}\) and FM spin correlation \(\langle {\hat{F}}_{jk}\rangle \approx 0.79\) on the x − (y-) type bonds as well as \(\langle {\hat{F}}_{jk}\rangle \approx 0.82\) on the z-type bonds. d Magnon bands within nonlinear SWT on a cylinder for the [111] ordered state. The chiral edge states are marked in green. The real-time dynamics of (e) spin current js(t, x) and (f) charge current jc(x, t) for a [111] ordered states within DMRG. For d–f, we set Γ = 0.05K and t = 10K. The self-consistent solution with δ = 0.01 gives kinetic hole energy \(\langle {\hat{P}}_{jk}\rangle \approx -0.93\times 1{0}^{-2}\) and FM spin correlation \(\langle {\hat{F}}_{jk}\rangle \approx 0.85\) on all three type bonds.
