论文标题
手性旋转液体，拓扑超导体和电荷密度波Chern绝缘子之间的差异和双重性
Deconfined criticalities and dualities between chiral spin liquid, topological superconductor and charge density wave Chern insulator
论文作者
论文摘要
我们提出了手性旋转液体（CSL），拓扑超导体（SC）和电荷密度波（CDW）之间的双重临界和三个临界理论，订购了Chern绝缘子，Chern Instrator，Chern Number $ C = 2 $ in Square，Triangular和Kagagome Lattices。三个CDW订单参数形成$ s^2 $或$ s^1 $的流形，具体取决于易于平面各向异性。 CDW订单的Skyrmion缺陷带有物理费用$ 2E $，其冷凝水导致拓扑超导体。 CDW-SC的转变与正方形晶格上Neel Order和Valence Bond固体订单之间的著名解剂量子关键点（DQCP）处于相同的通用类别。可以通过连续的相变从CSL相访问SC和CDW顺序。在CSL-SC过渡时，尽管两侧都没有CDW，但仍存在CDW阶波波动。我们为CSL-SC过渡提出了三种不同的理论（以及CSL到Easy-Plane CDW过渡）：一个带有两个玻色子的$ U（1）$理论，带有两个Dirac Fermions的$ U（1）$理论，以及一个带有两个玻色子的$ SU（2）$理论。我们的构建提供了这三种理论之间的双重性以及有希望的身体实现。 $ su（2）$理论为一系列具有显式$ so（5），o（4）$或$ SO（3）\ times o（2）$对称的固定点提供了一个统一的框架。还有一个透明的二元转换映射SC订单到Easy-Plane CDW顺序。在此二元映射下，CSL-SC-CDW三临界点是不变的，并且具有扩大的$（5）$或$ O（4）$对称性。 CDW和SC之间的DQCP继承了从三个临界点开始的扩大的对称性，新兴的异常和自以为是的。我们的分析将对称性阶段之间的良好研究的DQCP统一到一个更大的框架中，在该框架中它们距离拓扑有序相位。
We propose bi-critical and tri-critical theories between chiral spin liquid (CSL), topological superconductor (SC) and charge density wave (CDW) ordered Chern insulator with Chern number $C=2$ on square, triangular and kagome lattices. The three CDW order parameters form a manifold of $S^2$ or $S^1$ depending on whether there is easy-plane anisotropy. The skyrmion defect of the CDW order carries physical charge $2e$ and its condensation leads to a topological superconductor. The CDW-SC transitions are in the same universality classes as the celebrated deconfined quantum critical points (DQCP) between Neel order and valence bond solid order on square lattice. Both SC and CDW order can be accessed from the CSL phase through a continuous phase transition. At the CSL-SC transition, there is still CDW order fluctuations although CDW is absent in both sides. We propose three different theories for the CSL-SC transition (and CSL to easy-plane CDW transition): a $U(1)$ theory with two bosons, a $U(1)$ theory with two Dirac fermions, and an $SU(2)$ theory with two bosons. Our construction offers a derivation of the duality between these three theories as well as a promising physical realization. The $SU(2)$ theory offers a unified framework for a series of fixed points with explicit $SO(5), O(4)$ or $SO(3)\times O(2)$ symmetry. There is also a transparent duality transformation mapping SC order to easy-plane CDW order. The CSL-SC-CDW tri-critical points are invariant under this duality mapping and have an enlarged $SO(5)$ or $O(4)$ symmetry. The DQCPs between CDW and SC inherit the enlarged symmetry, emergent anomaly, and self-duality from the tri-critical point. Our analysis unifies the well-studied DQCP between symmetry breaking phases into a larger framework where they are proximate to a topologically ordered phase.
