Material realizations of the bond-dependent Kitaev interactions with $S=1/2$ local moments have vitalized the research in quantum spin liquids. Recently, it has been proposed that higher-spin analogs of the Kitaev interactions may also occur in a number of materials with strong spin-orbit coupling. In contrast to the celebrated $S=1/2$ Kitaev model on the honeycomb lattice, the higher-spin Kitaev models are not exactly solvable. Hence, the existence of quantum spin liquids in these systems remains an outstanding question. In this paper, we use the density matrix renormalization group methods to numerically investigate the $S=1$ Kitaev model with both ferromagnetic (FM) and antiferromagnetic (AFM) interactions. Using results on quasi-one-dimensional finite-size cylindrical geometries with circumferences of up to six legs, we conclude that the ground state of the $S=1$ Kitaev model is a quantum spin liquid with a ${\mathbb{Z}}_2$ gauge structure. We are also able to put an upper bound on the excitation gap. The magnetic field responses for the FM and AFM models are similar to those of the $S=1/2$ counterparts. In particular, in the AFM $S=1$ model, a gapless quantum spin-liquid state emerges in an intermediate window of magnetic field strength, before the system enters a trivial polarized state.

中文翻译：

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表征自旋一Kitaev量子自旋液体

与键有关的Kitaev相互作用的物质实现 $\mathrm{小号}=\mathrm{1个}/2$局部时刻激发了对量子自旋液体的研究。近来，已经提出在许多具有强自旋轨道耦合的材料中也可能出现Kitaev相互作用的高自旋类似物。与著名的相反$\mathrm{小号}=\mathrm{1个}/2$Kitaev模型位于蜂窝格子上，旋转速度更快的Kitaev模型并非完全可求解。因此，这些系统中量子自旋液体的存在仍然是一个悬而未决的问题。在本文中，我们使用密度矩阵重归一化组方法来数值研究$\mathrm{小号}=\mathrm{1个}$具有铁磁（FM）和反铁磁（AFM）相互作用的Kitaev模型。使用圆周最多为6条腿的准一维有限尺寸圆柱几何的结果，我们得出结论：$\mathrm{小号}=\mathrm{1个}$ Kitaev模型是一种量子自旋液体，具有 ${\mathbb{ž}}_2$量规结构。我们还可以在激励间隙上设置一个上限。FM和AFM模型的磁场响应与$\mathrm{小号}=\mathrm{1个}/2$同行。特别是在AFM中$\mathrm{小号}=\mathrm{1个}$ 在该模型中，在系统进入微不足道的极化状态之前，无隙量子自旋液体状态出现在磁场强度的中间窗口中。