Kitaev 蜂窝自旋液体的精确张量网络完整纠缠结构

中文摘要 AI 辅助

虽然 Kitaev 蜂窝模型的多数特征已通过 ${\mathbb Z}_2$ plaquette 和 Majorana 费米子图像得到阐明，但我们表明，恢复其精确的量子多体形式可为解决其自旋液体性质中的剩余问题提供线索。我们通过顺序量子数投影和 Gutzwiller 投影，从随机乘积态出发，提供了一组完整解的精确二维张量网络描述，这两种投影均表示为维度 $D=2$ 的局域矩阵乘积算符。基态和激发态共享相同的键维数，但表现出不同的 Schmidt 谱，从而区分了它们的面积律和体积律纠缠。我们证明，拓扑纠缠熵仅在 Gutzwiller 投影到物理自旋希尔伯特空间之后才对所有本征态出现，其中规范约束恰好移除了一半的 Schmidt 态。这确立了激发态同样具有拓扑序。我们进一步表明，在已知能很好描述自旋液体的 Parton 平均场态中，存在一种投影诱导的波函数坍缩到单一规范扇区的现象。在 $S=1/2$ 的 kagome 和三角 Heisenberg 模型上的演示表明，本视角可应用于更广泛的具有 ${\mathbb Z}_2$ 自旋液体的模型类别。我们的发现可视化了体-边界对应关系，并辅以 Wilson 环对拓扑序的表征。

英文摘要

While most of the features of the Kitaev honeycomb model are already clarified from the combined ${\mathbb Z}_2$ plaquette and Majorana fermion picture, we show that retrieving the exact quantum many-body form gives a clue to fix the remaining issues on its spin liquid property. We provide an exact two-dimensional tensor network description of a full set of solutions from a random product state, by sequential quantum-number projection and Gutzwiller projection, both expressed as local matrix-product operators of dimension $D=2$. The ground and excited states share the same bond dimension yet exhibit distinct Schmidt spectra, distinguishing their area-law and volume-law entanglement. We demonstrate that the topological entanglement entropy emerges {\it for all eigenstates only after} the Gutzwiller projection onto the physical spin Hilbert space, where the gauge constraint removes exactly half of the Schmidt states. This establishes that excited states are likewise topologically ordered. We further show that there exists a projection-induced collapse of the wave function into a single gauge sector in the Parton mean-field states that is known to give a good description of the spin liquids. The demonstrations on the $S=1/2$ kagome and triangular Heisenberg models suggest that the present perspective is applied to a wider class of models hosting ${\mathbb Z}_2$ spin liquids. Our finding visualizes a bulk-boundary correspondence with the Wilson-loop characterization of topological order.

发表机构

• University of Tokyo（东京大学）

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