PhD论文：寻找真实材料中涌现的SU（4）对称性
PhD Thesis: Searching for an emergent SU(4) symmetry in real materials
摘要：
利用$N>2$将自旋空间对称性从通常的$\mathrm{SU}(2)$增强到$\mathrm{SU}(N)$，对于寻找非平凡的量子自旋液体是有希望的，但是在实际材料中实现$\mathrm{SU}(N)$自旋系统仍然是具有挑战性的。虽然在冷原子系统中有一个建议，但在具有自旋-轨道自由度的磁性材料中，很难通过微调来实现$\mathrm{SU}(N)$对称性。在这里，我们提出了一个新的机制，$\mathrm{SU}(4)$对称性出现在强自旋轨道耦合极限。在具有共边阴离子八面体的$d^1$过渡金属化合物中，自旋-轨道耦合在$J_\textrm{eff}=3/2$四重态之间产生强烈的键依赖性和明显的$\mathrm{SU}(4)$ -断裂跳跃。然而，在蜂窝结构中，规范变换将系统映射到$\mathrm{SU}(4)$对称的Hubbard模型，这意味着尽管系统具有大的自旋-轨道耦合，但系统具有隐藏的对称性。在四分之一填充时的强排斥极限中，如在$α$ -ZrCl $_3,$中所预期的，低能有效模型是蜂窝晶格上的$\mathrm{SU}(4)$海森堡模型，其不能具有平凡的带隙基态，并且预期容纳无带隙的自旋轨道液体。在这种量子自旋轨道液体中，由于它们之间的强阻挫相互作用，自旋和轨道自由度在低温下变得分数化并关联在一起。类似于纯量子自旋液体中的自旋子，量子自旋轨道液体不仅可以承载自旋子激发，而且可以在低温下承载费米子“轨道子”激发，我们在这里将其命名为与在量子破碎的Jahn-Teller相中的轨道不同。
英文摘要：
The enhancement of the spin-space symmetry from the usual $\mathrm{SU}(2)$ to $\mathrm{SU}(N)$ with $N>2$ is promising for finding nontrivial quantum spin liquids, but the realization of $\mathrm{SU}(N)$ spin systems in real materials is still challenging. Although there is a proposal in cold atomic systems, in magnetic materials with a spin-orbital degree of freedom it is difficult to achieve the $\mathrm{SU}(N)$ symmetry by fine tuning. Here we propose a new mechanism by which the $\mathrm{SU}(4)$ symmetry emerges in the strong spin-orbit coupling limit. In $d^1$ transition metal compounds with edge-sharing anion octahedra, the spin-orbit coupling gives rise to strongly bond-dependent and apparently $\mathrm{SU}(4)$-breaking hopping between the $J_\textrm{eff}=3/2$ quartets. However, in the honeycomb structure, a gauge transformation maps the system to an $\mathrm{SU}(4)$-symmetric Hubbard model, which means that the system has a hidden symmetry in spite of its large spin-orbit coupling. In the strong repulsion limit at quarter filling, as expected in $α$-ZrCl$_3,$ the low-energy effective model is the $\mathrm{SU}(4)$ Heisenberg model on the honeycomb lattice, which cannot have a trivial gapped ground state and is expected to host a gapless spin-orbital liquid. In such quantum spin-orbital liquids, both the spin and orbital degrees of freedom become fractionalized and correlated together at low temperature due to the strong frustrated interactions between them. Similarly to spinons in pure quantum spin liquids, quantum spin-orbital liquids can host not only spinon excitations, but also fermionic "orbitalon" excitations at low temperature, which we have named here in distinction from orbitons in the symmetry-broken Jahn-Teller phases.
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