From Luttinger liquid to non-Abelian quantum Hall states

By J. C. Teo, C. L. Kane. 2011

171 citations recorded by the source corpus.

We formulate a theory of non-Abelian fractional quantum Hall states by considering an anisotropic system consisting of coupled, interacting one dimensional wires. We show that Abelian bosonization provides a simple framework for characterizing the Moore Read state, as well as the more general Read Rezayi sequence. This coupled wire construction provides a solvable Hamiltonian formulated in terms of electronic degrees of freedom, and provides a direct route to characterizing the quasiparticles and edge states in terms of conformal field theory. This construction leads to a simple interpretation of the coset construction of conformal field theory, which is a powerful method for describing non Abelian states. In the present context, the coset construction arises when the original chiral modes are fractionalized into coset sectors, and the different sectors acquire energy gaps due to coupling in "different directions". The coupled wire construction can also can be used to describe anisotropic lattice systems, and provides a starting point for models of fractional and non-Abelian Chern insulators. This paper also includes an extended introduction to the coupled wire construction for Abelian quantum Hall states, which was introduced earlier.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/26fb0ba4b85bffa5d469516abf96760ff1f7d8f1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. J. Alicea
2. N. Lindner
3. A. Stern
4. C. Nayak
5. P. Fendley
6. Tanmoy Das
7. Roger S. K. Mong
8. Erez Berg

In Condensed Matter Physics

1. J. Alicea
2. Roger S. K. Mong
3. A. Stern
4. C. Nayak
5. Hsin Lin
6. Matthew Fisher
7. P. Fendley
8. N. Lindner

Citations in the corpus

• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure (2013, methodology): “We follow a different approach inspired by Teo and Kane’s method of obtaining nonAbelian quantum Hall phases from stacks of weakly coupled Luttinger liquids [97].”
• Colloquium : Topological band theory (2016, background): “…Kitaev 2009; Schnyder et al. 2008), axions,(Essin, Moore, and Vanderbilt 2009; Li et al. 2010) magnetic monopoles, (Qi, Li, et al. 2009) fractional excitations (Wen 1995; Grushin et al. 2012; Li, Liu, et al. 2014; Teo and Kane 2014), which are not amenable to treatment on a first-principles basis.”