aqora

Pattern of Zeros

Modjtaba Shokrian Zini, Zhenghan Wang, Xiao-Gang Wen

In this paper, we provide a set of definitions upon which one can prove in a rigorous way most of the main results achieved in the pattern of zeros classification of fractional quantum Hall states.

arXiv:1711.05937Nov 16, 20170 citations

Pattern-of-Zeros Approach to Fractional Quantum Hall States and a Classification of Symmetric Polynomial of Infinite Variables

Xiao-Gang Wen, Zhenghan Wang

arXiv:1203.3268Mathematical lectures from Peking UniversityOct 30, 20134 citations

Classification of Abelian and non-Abelian multilayer fractional quantum Hall states through the pattern of zeros

Maissam Barkeshli, Xiao-Gang Wen

A large class of fractional quantum Hall (FQH) states can be classified according to their pattern of zeros, which describes the way ideal ground-state wave functions go to zero as various clusters of electrons are brought together. In this paper, we generalize this approach to classify multilayer FQH states. Such a classification leads to the construction of a class of non-Abelian multilayer FQH states that are closely related to ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{g}}_{k}$ parafermion conformal field theories, where ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{g}}_{k}$ is an affine simple Lie algebra. We discuss the possibility of some of the simplest of these non-Abelian states occurring in experiments on bilayer FQH systems at $\ensuremath{\nu}=2/3$, 4/5, 4/7, etc.A large class of fractional quantum Hall (FQH) states can be classified according to their pattern of zeros, which describes the way ideal ground-state wave functions go to zero as various clusters of electrons are brought together. In this paper, we generalize this approach to classify multilayer FQH states. Such a classification leads to the construction of a class of non-Abelian multilayer FQH states that are closely related to ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{g}}_{k}$ parafermion conformal field theories, where ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{g}}_{k}$ is an affine simple Lie algebra. We discuss the possibility of some of the simplest of these non-Abelian states occurring in experiments on bilayer FQH systems at $\ensuremath{\nu}=2/3$, 4/5, 4/7, etc.

arXiv:0906.0337Physical Review BDec 2, 201025 citations

The existence and stability of fractional quantum Hall states

A M Reynolds

[Please see PDF for abstract.]

Sep 14, 20260 citations

Structure of quasiparticles and their fusion algebra in fractional quantum Hall states

Maissam Barkeshli, Xiao-Gang Wen

It was recently discovered that fractional quantum Hall (FQH) states can be characterized quantitatively by the pattern of zeros that describe how the ground-state wave function goes to zero when electrons are brought close together. Quasiparticles in the FQH states can be described in a similar quantitative way by the pattern of zeros that result when electrons are brought close to the quasiparticles. In this paper, we combine the pattern of zeros approach and the conformal field theory (CFT) approach to calculate the topological properties of quasiparticles. We discuss how the quasiparticles in FQH states naturally form representations of a magnetic translation algebra, with members of a representation differing from each other by Abelian quasiparticles. We find that this structure dramatically simplifies topological properties of the quasiparticles, such as their fusion rules, charges, and scaling dimensions, and has consequences for the ground state degeneracy of FQH states on higher genus surfaces. We find constraints on the pattern of zeros of quasiparticles that can fuse together, which allow us to derive the fusion rules of quasiparticles from their pattern of zeros, at least in the case of the (generalized and composite) parafermion states. We also calculate from CFT the number of quasiparticle types in the generalized and composite parafermion states, which confirm the result obtained previously through a completely different approach.It was recently discovered that fractional quantum Hall (FQH) states can be characterized quantitatively by the pattern of zeros that describe how the ground-state wave function goes to zero when electrons are brought close together. Quasiparticles in the FQH states can be described in a similar quantitative way by the pattern of zeros that result when electrons are brought close to the quasiparticles. In this paper, we combine the pattern of zeros approach and the conformal field theory (CFT) approach to calculate the topological properties of quasiparticles. We discuss how the quasiparticles in FQH states naturally form representations of a magnetic translation algebra, with members of a representation differing from each other by Abelian quasiparticles. We find that this structure dramatically simplifies topological properties of the quasiparticles, such as their fusion rules, charges, and scaling dimensions, and has consequences for the ground state degeneracy of FQH states on higher genus surfaces. We find constraints on the pattern of zeros of quasiparticles that can fuse together, which allow us to derive the fusion rules of quasiparticles from their pattern of zeros, at least in the case of the (generalized and composite) parafermion states. We also calculate from CFT the number of quasiparticle types in the generalized and composite parafermion states, which confirm the result obtained previously through a completely different approach.

arXiv:0807.2789Physical Review BMay 29, 200938 citations

Introduction to the Topic of Jack Polynomials in the Context of Fractional Quantum Hall Effect

Bartosz Kuśmierz, Arkadiusz Wójs

Nov 26, 20170 citations

Pattern of Zeros

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Pattern of Zeros

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