U(1)xU(1)xZ{sub 2} Chern-Simons theory and Z{sub 4} parafermion fractional quantum Hall states

Journal Article · Fri Jan 15 00:00:00 EST 2010 · Physical Review. B, Condensed Matter and Materials Physics

DOI:https://doi.org/10.1103/PHYSREVB.81.045323· OSTI ID:21366669

Barkeshli, Maissam; Xiaogang, Wen ^[1]

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1. Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)

We study U(1)xU(1)xZ{sub 2} Chern-Simons theory with integral coupling constants (k,l) and its relation to certain non-Abelian fractional quantum Hall (FQH) states. For the U(1)xU(1)xZ{sub 2} Chern-Simons theory, we show how to compute the dimension of its Hilbert space on genus g surfaces and how this yields the quantum dimensions of topologically distinct excitations. We find that Z{sub 2} vortices in the U(1)xU(1)xZ{sub 2} Chern-Simons theory carry non-Abelian statistics and we show how to compute the dimension of the Hilbert space in the presence of n pairs of Z{sub 2} vortices on a sphere. These results allow us to show that l=3 U(1)xU(1)xZ{sub 2} Chern-Simons theory is the low-energy effective theory for the Z{sub 4} parafermion (Read-Rezayi) fractional quantum Hall states, which occur at filling fraction nu=(2/2k-3). The U(1)xU(1)xZ{sub 2} theory is more useful than an alternative SU(2){sub 4}xU(1)/U(1) Chern-Simons theory because the fields are more closely related to physical degrees of freedom of the electron fluid and to an Abelian bilayer phase on the other side of a two-component to single-component quantum phase transition. We discuss the possibility of using this theory to understand further phase transitions in FQH systems, especially the nu=2/3 phase diagram.

• OSTI ID: 21366669
• Journal Information: Physical Review. B, Condensed Matter and Materials Physics, Vol. 81, Issue 4; Other Information: DOI: 10.1103/PhysRevB.81.045323; (c) 2010 The American Physical Society; ISSN 1098-0121
• Country of Publication: United States
• Language: English

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