标题： 拓扑纠缠熵的玻色-哈伯德自旋液体 显示英文标题

标题： Topological Entanglement Entropy of a Bose-Hubbard Spin Liquid

摘要： 通过破缺对称性来分类相的朗道范式被证明是不完整的，因为当意识到不同的量子霍尔态只能通过更微妙的拓扑性质来区分时，这一点得到了证实。 如今，拓扑作为秩序的基础描述的角色已经扩展到包括拓扑能带绝缘体，以及某些具有基态波函数拓扑简并的无特征的间隙莫特绝缘体。 尽管进行了大量研究，但这些拓扑有序的“自旋液体”候选者却非常少。 寻找包含自旋液体态的系统的主要困难在于它们违反了朗道范式，使得传统的序参量不存在。 在这里，我们在kagome晶格上的玻色-哈伯德模型中揭示了一个自旋液体相，并通过拓扑纠缠熵直接测量了其拓扑序。 这是首次通过其纠缠熵被识别为具有Z2规范对称性的间隙基态的非平凡自旋液体的明确证据。 显示英文摘要

摘要： The Landau paradigm of classifying phases by broken symmetries was demonstrated to be incomplete when it was realized that different quantum Hall states could only be distinguished by more subtle, topological properties. Today, the role of topology as an underlying description of order has branched out to include topological band insulators, and certain featureless gapped Mott insulators with a topological degeneracy in the groundstate wavefunction. Despite intense focus, very few candidates for these topologically ordered "spin liquids" exist. The main difficulty in finding systems that harbour spin liquid states is the very fact that they violate the Landau paradigm, making conventional order parameters non-existent. Here, we uncover a spin liquid phase in a Bose-Hubbard model on the kagome lattice, and measure its topological order directly via the topological entanglement entropy. This is the first smoking-gun demonstration of a non-trivial spin liquid, identified through its entanglement entropy as a gapped groundstate with emergent Z2 gauge symmetry.