Nambu 3-代数几何上的手征拓扑绝缘体
Chiral Topological Insulator on Nambu 3-Algebraic Geometry
摘要：
基于Nambu 3-代数几何构造了具有Landau能级的手征拓扑绝缘体（AIII类）.在四维量子霍尔效应的非对易几何背景下，阐明了AIII类拓扑绝缘体手征对称性的几何起源.多体基态波函数被明确地导出为具有唯一$K$矩阵结构的$(l,l,l-1)$ Laughlin-Halperin型波函数。基本激发被识别为具有分数电荷${1}/({1+2(l-1)^2})$的任意弦状物体。手性拓扑绝缘体的霍尔效应是霍尔效应的一种颜色版本，具有霍尔效应和自旋霍尔效应的双重性质。
英文摘要：
Chiral topological insulator (AIII-class) with Landau levels is constructed based on the Nambu 3-algebraic geometry. We clarify the geometric origin of the chiral symmetry of the AIII-class topological insulator in the context of non-commutative geometry of 4D quantum Hall effect. The many-body groundstate wavefunction is explicitly derived as a $(l,l,l-1)$ Laughlin-Halperin type wavefunction with unique $K$-matrix structure. Fundamental excitation is identified with anyonic string-like object with fractional charge ${1}/({1+2(l-1)^2})$. The Hall effect of the chiral topological insulators turns out be a color version of Hall effect, which exhibits a dual property of the Hall and spin-Hall effects.
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