Simplex Z_2 spin liquids on the Kagome lattice with Entangled Pair States: spinon and vison coherence lengths, topological entropy and gapless edge modes
Didier Poilblanc, Norbert Schuch
备注：
5 pages, 6 figures - v2 with moderate revision of abstract, text and conclusion
Gapped Z_2 spin liquids have been proposed as candidates for the ground-state of the S=1/2 quantum antiferromagnet on the Kagome lattice. We extend the use of Projected Entangled Pair States to construct (on the cylinder)Resonating Valence Bond (RVB) states including both nearest-neighbor and next-nearest neighbor singlet bonds. Our ansatz -- dubbed "simplex spin liquid" -- allows for an asymmetry between the two types of triangles (of order 2-3% in the energy density after optimization) leading to the breaking of inversion symmetry. We show that the topological Z_2 structure is still preserved and, by considering the presence or the absence of spinon and vison lines along an infinite cylinder, we explicitly construct four orthogonal RVB Minimally Entangled States. The spinon and vison coherence lengths are extracted from a finite size scaling w.r.t the cylinder perimeter of the energy splittings of the four sectors and are found to be of the order of the lattice spacing. The entanglement spectrum of a partitioned (infinite) cylinder is found to be gapless suggesting the occurrence, on a cylinder with {\it real} open boundaries, of gapless edge modes formally similar to Luttinger liquid (non-chiral) spin and charge modes. When inversion symmetry is spontaneously broken, the RVB spin liquid exhibits an extra Ising degeneracy, which might have been observed in recent exact diagonalisation studies.
Topological spinon bands and vison excitations in spin-orbit coupled quantum spin liquids
自旋液体是奇异的量子态，其特征在于存在分数和非限定的准粒子激发，称为自旋子和介子。它们的分数性质建立了拓扑性质，如受保护的基态简并。本文研究自旋-轨道耦合自旋液体，其中拓扑结构通过自旋子的非平凡能带结构进入。当自旋旋转对称性被最大限度地提升时，我们重新审视了最近在正方形晶格上的投影群分析中识别的$Z_2$自旋液相[Phys. Rev. B 90，174417（2014）]。我们发现，在只有最近邻耦合的情况下，正方晶格上的$Z_2$自旋液体总是表现出平凡的自旋带。加入第二近邻项后，最简单的射影群解非常类似于拓扑绝缘体的Bernevig-Hughes-Zhang模型。假设突现规范场是静态的，我们研究了视子激发，我们证实了在所有研究的自旋相位是去限制的。特别地，如果自旋带是拓扑的，自旋子和介子形成由多个自旋-马约拉纳零模耦合到一个介子组成的束缚态。这种零模的存在遵循这些自旋相位和具有涡旋的拓扑$p+ip$超导体之间的精确映射。我们提出了实验探针来检测这种状态在真实的材料。
Anderson localization of emergent quasiparticles: Spinon and vison interplay at finite temperature in a $\mathbb{Z}_2$ gauge theory in three dimensions
Transient localization from fractionalization: vanishingly small heat conductivity in gapless quantum magnets
Technical University of Munich（慕尼黑工业大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与工程中心）；The Ohio State University（俄亥俄州立大学）；Imperial College London（帝国理工学院）
Investigation of the $J_1$-$J_2$ Heisenberg model on the triangular lattice: A study with projected entangled-pair states
Sun Yat-sen University（中山大学）；Keio University（庆应义塾大学）；Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, CNRS, UPS, France（图卢兹大学理论物理实验室，IRSAMC，CNRS，UPS）
