Eight-Dimensional Quantum Hall Effect and "Octonions"

Bogdan A. Bernevig; Jiangping Hu; Nicolaos Toumbas; Shou Cheng Zhang

Eight-Dimensional Quantum Hall Effect and "Octonions"

Bogdan A. Bernevig, Jiangping Hu, Nicolaos Toumbas, Shou Cheng Zhang

Research output: Contribution to journal › Article › peer-review

Abstract

A generalization of the quantum Hall effect (QHE) where particles move in an eight-dimensional space under an SO(8) gauge field was constructed. A nonrelativistic Hamiltonian for particles moving on the S⁸ in the presence of the SO(8) gauge field above was also introduced. The particle carry SO(8) numbers and the generators ∑_μν, combine nontrivally with the orbital angular momentum L_μν⁽⁰⁾ on the equator of S⁸, to select some distinct special representations of the SO(9) L_ab which label the particle. The two eight-dimensional quantum Hall fluids, whose dimensions vary as R²⁰ and R ¹⁴, were also constructed.

Original language	English (US)
Article number	236803
Pages (from-to)	2368031-2368034
Number of pages	4
Journal	Physical review letters
Volume	91
Issue number	23
State	Published - Dec 5 2003
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Physics and Astronomy

Cite this

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AU - Bernevig, Bogdan A.

AU - Hu, Jiangping

AU - Toumbas, Nicolaos

AU - Zhang, Shou Cheng

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Y1 - 2003/12/5

N2 - A generalization of the quantum Hall effect (QHE) where particles move in an eight-dimensional space under an SO(8) gauge field was constructed. A nonrelativistic Hamiltonian for particles moving on the S8 in the presence of the SO(8) gauge field above was also introduced. The particle carry SO(8) numbers and the generators ∑μν, combine nontrivally with the orbital angular momentum Lμν(0) on the equator of S8, to select some distinct special representations of the SO(9) Lab which label the particle. The two eight-dimensional quantum Hall fluids, whose dimensions vary as R20 and R 14, were also constructed.

AB - A generalization of the quantum Hall effect (QHE) where particles move in an eight-dimensional space under an SO(8) gauge field was constructed. A nonrelativistic Hamiltonian for particles moving on the S8 in the presence of the SO(8) gauge field above was also introduced. The particle carry SO(8) numbers and the generators ∑μν, combine nontrivally with the orbital angular momentum Lμν(0) on the equator of S8, to select some distinct special representations of the SO(9) Lab which label the particle. The two eight-dimensional quantum Hall fluids, whose dimensions vary as R20 and R 14, were also constructed.

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Eight-Dimensional Quantum Hall Effect and "Octonions"

Abstract

All Science Journal Classification (ASJC) codes

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