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Some aspects of the problem in the four-dimensional quantum Hall effect

Record Type:	Electronic resources : Monograph/item
Title/Author:	Some aspects of the problem in the four-dimensional quantum Hall effect
Author:	Chern, Chyh-Hong.
Description:	93 p.
Notes:	Adviser: Shoucheng Zhang.
Notes:	Source: Dissertation Abstracts International, Volume: 65-04, Section: B, page: 1916.
Contained By:	Dissertation Abstracts International65-04B.
Subject:	Physics, Condensed Matter.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3128363
ISBN:	0496756257

Some aspects of the problem in the four-dimensional quantum Hall effect
Chern, Chyh-Hong.

Some aspects of the problem in the four-dimensional quantum Hall effect [electronic resource] - 93 p.

Adviser: Shoucheng Zhang.

Thesis (Ph.D.)--Stanford University, 2004.

The remarkable Landau level structure can be generalized to 4-sphere with SU(2) magnetic monopole at the center of the 4-sphere. The bulk states reveal the relativistic nature if we maximally enlarge the gauge symmetry to the one of this system, which is SO(5). When the monopole strength S is less than or equal to 2, they describe the helicity states of massless particles of spin. Moreover, the effective field theory of the lowest Landau level is formulated on CP3, which is the level manifold of the lowest Landau level. The single particle Lagrangian is the Berry's phase over CP3. Using the flux attachment transformation, the hydrodynamic description of this model can be written as a 6+1 dimensional U(1) Chem-Simons theory. Locally, the system can be regarded as three independent 2-dimensional quantum Hall planes. Because the choice of the independent planes is arbitrary up to a gauge transformation, the interchanging phase between membranes can be defined on CP3 by moving one membrane around the other on a 2DQHE plane. They are the elementary excitations of the system and may obey fractional statistics, if the system is fractionally filled.

ISBN: 0496756257Subjects--Topical Terms:

226939
Physics, Condensed Matter.

Some aspects of the problem in the four-dimensional quantum Hall effect
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520 # $a The remarkable Landau level structure can be generalized to 4-sphere with SU(2) magnetic monopole at the center of the 4-sphere. The bulk states reveal the relativistic nature if we maximally enlarge the gauge symmetry to the one of this system, which is SO(5). When the monopole strength S is less than or equal to 2, they describe the helicity states of massless particles of spin. Moreover, the effective field theory of the lowest Landau level is formulated on CP3, which is the level manifold of the lowest Landau level. The single particle Lagrangian is the Berry's phase over CP3. Using the flux attachment transformation, the hydrodynamic description of this model can be written as a 6+1 dimensional U(1) Chem-Simons theory. Locally, the system can be regarded as three independent 2-dimensional quantum Hall planes. Because the choice of the independent planes is arbitrary up to a gauge transformation, the interchanging phase between membranes can be defined on CP3 by moving one membrane around the other on a 2DQHE plane. They are the elementary excitations of the system and may obey fractional statistics, if the system is fractionally filled.
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