Chiral topological insulator on Nambu 3-algebraic geometry

Chiral topological insulator (All-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/(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. (C) 2014 The Author. Published by Elsevier B.V.