Geometric construction of the Quantum Hall Effect in all even dimensions

Details Geometric construction of the Quantum Hall Effect in all even dimensions Geometric construction of the Quantum Hall Effect in all even dimensions

2003-06-13

arxiv.org/abs/cond-mat/0306351v4

J.Phys.A36:9415-9424,2003

Physics

Condensed Matter

11 pages, the final published version

Scientific paper

10.1088/0305-4470/36/36/301

The Quantum Hall Effects in all even dimensions are uniformly constructed. Contrary to some recent accounts in the literature, the existence of Quantum Hall Effects does not {\it crucially} depend on the existence of division algebras. For QHE on flat space of even dimensions, both the Hamiltonians and the ground state wave-functions for a single particle are explicitly described. This explicit description immediately tells us that QHE on a higher even dimensional flat space shares the common features such as incompressibility with QHE on plane.

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