Layered material $\alpha \text{−}{\mathrm{RuCl}}_3$ has caught wide attention due to its possible realization of Kitaev's spin liquid and its electronic structure that involves the interplay of electron-electron correlations and spin-orbit effects. Several $\mathrm{DFT}+U$ studies have suggested that both electron-electron correlations and spin-orbit effects are crucial for accurately describing the band gap. This work studies the importance of these two effects using fixed-node and fixed-phase diffusion Monte Carlo calculations both in spin-averaged and explicit spin-orbit formalisms. In the latter, the Slater-Jastrow trial function is constructed from two-component spin orbitals using our recent quantum Monte Carlo (QMC) developments and thoroughly tested effective core potentials. Our results show that the gap in the ideal crystal is already accurately described by the spin-averaged case, with the dominant role being played by the magnetic ground state with significant exchange and electron correlation effects. We find qualitative agreement between hybrid DFT, $\text{DFT}+U$, and QMC. In addition, QMC results agree very well with available experiments, and we identify the values of exact Fock exchange mixing that provide comparable gaps. Explicit spin-orbit QMC calculations reveal that the effect of spin-orbit coupling on the gap is minor, of the order of 0.2 eV, which corresponds to the strength of the spin orbit of the Ru atom.

中文翻译：

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固定节点和固定相位扩散蒙特卡罗方法的α-RuCl3电子结构

分层材料$\alpha \text{-}{\mathrm{氯化钌}}_3$由于其可能实现基塔耶夫的自旋液体及其涉及电子-电子相关性和自旋轨道效应相互作用的电子结构，引起了广泛关注。一些$\mathrm{密度泛函}+ü$研究表明，电子 - 电子相关性和自旋轨道效应对于准确描述带隙至关重要。这项工作使用自旋平均和显式自旋轨道形式中的固定节点和固定相位扩散蒙特卡罗计算来研究这两种效应的重要性。在后者中，Slater-Jastrow 试验函数是使用我们最近的量子蒙特卡罗 (QMC) 开发并彻底测试了有效核心电位的双分量自旋轨道构建的。我们的结果表明，理想晶体中的间隙已经由自旋平均情况准确描述，其中主要作用由具有显着交换和电子相关效应的磁性基态发挥。我们发现混合 DFT 之间的定性一致，$\text{密度泛函}+ü$，和 QMC。此外，QMC 结果与现有实验非常吻合，我们确定了提供可比差距的精确 Fock 交换混合的值。明确的自旋轨道 QMC 计算表明，自旋轨道耦合对间隙的影响很小，约为 0.2 eV，这对应于 Ru 原子自旋轨道的强度。