Chiral topological insulator on Nambu 3-algebraic geometry

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)(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/(2(l−1)2+1)1/(2(l−1)2+1). 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.