自旋向列相中由向错晶格量子熔化产生的拓扑序
Topological order in spin nematics from the quantum melting of a disclination lattice
AI总结：
本文研究二维自旋向列相中向错晶格的量子熔化，提出不可压缩向错量子液体作为稳定低温相，具有拓扑序、分数化准粒子和受保护边缘模，并通过Z₂规范理论的连续极限分析及微观模型构建加以论证。
摘要：
二维空间中自旋(n+1)向列相的拓扑缺陷，即向错，对于n≥2，由π₁(RPⁿ)=Z₂同伦群表征。我们认为，向错的不可压缩量子液体可以作为稳定的低温相存在，并承载复合准粒子，这些准粒子结合了基本Z₂电荷的分数部分与单位拓扑电荷。环面上四重拓扑基态简并允许费米子或半子准粒子交换统计。这些态的拓扑非平凡性体现在受保护的零能隙边缘模的存在上。虽然费米子向列相和有能隙的Z₂自旋液体具有等价的拓扑序，但由于具有不同的边缘模，它们在热力学上仍然不同，类似于量子自旋霍尔系统的拓扑非平凡态和拓扑平凡态。分析通过将自旋向列相的Z₂规范理论重新表述为具有更大规范结构的连续极限理论来进行。向列相分数化与量子霍尔液体相似，但大的规范对称性恢复了时间反演对称性，并限制了准粒子的融合规则和统计。场论分析的结论辅以合理宿主微观模型的构建。
英文摘要：
The topological defects of Spin($n+1$) nematics in two spatial dimensions, known as disclinations, are characterized by the $π_1(\mathbb{R}P^n) = \textrm{Z}_2$ homotopy group for $n\ge2$. We argue that incompressible quantum liquids of disclinations can exist as stable low-temperature phases and host composite quasiparticles which combine a fractional amount of fundamental Z$_2$ charge with a unit of topological charge. The four-fold topological ground state degeneracy on a torus admits a fermionic or semionic quasiparticle exchange statistics. The topological non-triviality of these states is visible in the existence of protected gapless edge modes. While the fermionic nematic and gapped Z$_2$ spin liquids have equivalent topological orders, they are still thermodynamically distinct due to having different edge modes, in analogy to the topologically non-trivial and trivial states of quantum spin-Hall systems. The analysis proceeds by recasting the Z$_2$ gauge theory of spin nematics as a continuum limit theory with a larger gauge structure. Nematic fractionalization parallels that of a quantum Hall liquid, but the large gauge symmetry restores the time-reversal symmetry and restricts the quasiparticle fusion rules and statistics. The conclusions from field theory analysis are complemented with the construction of plausible host microscopic models.
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