# Non-Abelian fermionization and the landscape of quantum Hall phases

@article{Goldman2020NonAbelianFA,
title={Non-Abelian fermionization and the landscape of quantum Hall phases},
author={Hart Goldman and Raman Sohal and Eduardo Fradkin},
journal={arXiv: Strongly Correlated Electrons},
year={2020}
}
• Published 31 August 2020
• Physics
• arXiv: Strongly Correlated Electrons
The recent proposal of non-Abelian boson-fermion dualities in 2+1 dimensions, which morally relate $U(k)_N$ to $SU(N)_{-k}$ Chern-Simons-matter theories, presents a new platform for exploring the landscape of non-Abelian quantum Hall states accessible from theories of Abelian composite particles. Here we focus on dualities relating theories of Abelian quantum Hall states of bosons or fermions to theories of non-Abelian "composite fermions" partially filling Landau levels. We show that these…
1 Citations

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## References

SHOWING 1-10 OF 63 REFERENCES
Level/rank duality and Chern-Simons-matter theories
• Physics
• 2016
A bstractWe discuss in detail level/rank duality in three-dimensional Chern-Simons theories and various related dualities in three-dimensional Chern-Simons-matter theories. We couple the dual
Baryons, monopoles and dualities in Chern-Simons-matter theories
A bstractThere is significant evidence for a duality between (non-supersymmetric) U(N ) Chern-Simons theories at level k coupled to fermions, and U(k) Chern-Simons theories at level N coupled to
Projective construction of non-Abelian quantum Hall liquids
Using projective construction, a generalized parton construction, we construct many non-Abelian quantum Hall (QH) states, which include the Pfaffian state at filling fraction $\ensuremath{\nu}=1/2.$
Non-Abelian statistics in the fractional quantum Hall states.
• Wen
• Physics, Medicine
Physical review letters
• 1991
The Fractional Quantum Hall states with non-Abelian statistics are studied and it is argued that the topological orders and the associated properties are robust against any kinds of small perturbations.
Landau-Ginzburg theories of non-Abelian quantum Hall states from non-Abelian bosonization
• Physics
Physical Review B
• 2019
It is an important open problem to understand the landscape of non-Abelian fractional quantum Hall phases which can be obtained starting from physically motivated theories of Abelian composite
Abelian topological order of ν=2/5 and 3/7 fractional quantum Hall states in lattice models
• Physics
• 2021
Determining the statistics of elementary excitations supported by fractional quantum Hall states is crucial to understanding their properties and potential applications. In this paper, we use the
Emergent QCD3 quantum phase transitions of fractional Chern insulators
• Physics
• 2020
Motivated by the recent work of QED$_3$-Chern-Simons quantum critical points of fractional Chern insulators (Phys. Rev. X \textbf{8}, 031015, (2018)), we study its non-Abelian generalizations, namely
Flavor broken QCD3 at large N
We examine the vacuum structure of QCD$_3$ with flavor group $U(f)\times U(N_f-f)$ in the limit $N\to\infty$ with $g^2N=$fixed. We find that, generically, the resolution of critical points into a
Noncommutative field theory and composite Fermi liquids in some quantum Hall systems
• Physics
• 2020
Composite Fermi liquid metals arise at certain special filling fractions in the quantum Hall regime and play an important role as parent states of gapped states with quantized Hall response. They
Charting the phase diagram of QCD3
• Physics
Journal of High Energy Physics
• 2019
Abstract We study the phase diagram of SU (N) gauge theory in three space-time dimensions with a Chern-Simons term at level k, coupled to two sets of fundamental fermions with masses m 1 and m