Non-Abelian Fermionization and Fractional Quantum Hall Transitions

Abstract

There has been a recent surge of interest in dualities relating theories of Chern-Simons gauge fields coupled to either bosons or fermions within the condensed matter community, particularly in the context of topological insulators and the half-filled Landau level. Here, we study the application of one such duality to the long-standing problem of quantum Hall inter-plateaux transitions. The key motivating experimental observations are the anomalously large value of the correlation length exponent $\nu \approx 2.3$ and that $\nu$ is observed to be super-universal, i.e., the same in the vicinity of distinct critical points. Duality motivates effective descriptions for a fractional quantum Hall plateau transition involving a Chern-Simons field with $U(N_c)$ gauge group coupled to $N_f=1$ fermion. We study one class of theories in a controlled limit where $N_f\gg N_c$ and calculate $\nu$ to leading non-trivial order in the absence of disorder. Although these theories do not yield an anomalously large exponent $\nu$ within the large $N_f\gg N_c$ expansion, they do offer a new parameter space of theories that is apparently different from prior works involving abelian Chern-Simons gauge fields.

9 pages, 2 figures, fixed typos and clarified notation

References in corpus (3)

• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Level/rank Duality and Chern-Simons-Matter Theories
• Composite fermion duality for half-filled multicomponent Landau Levels

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• On the Higher Spin Spectrum of Chern-Simons Theory coupled to Fermions in the Large Flavour Limit
• An all order exact result for the anomalous dimension of the scalar primary in Chern Simons Vector Models
• Lattice Construction of Duality with Non-Abelian Gauge Fields in 2+1D
• Duality Web on a 3D Euclidean Lattice and Manifestation of Hidden Symmetries
• Continuous transition between Ising magnetic order and a chiral spin liquid
• Scaling and Diffusion of Dirac Composite Fermions