Non-Abelian bosonization and modular transformation approach to superuniversality

Abstract

Quantum Hall inter-plateaux transitions are physical exemplars of quantum phase transitions. Near each of these transitions, the measured electrical conductivity scales with the same correlation length and dynamical critical exponents, i.e., the critical points are superuniversal. In apparent contradiction to these experiments, prior theoretical studies of quantum Hall phase transitions within the framework of Abelian Chern-Simons theory coupled to matter found correlation length exponents that depend on the value of the quantum critical Hall conductivity. Here, we use non-Abelian bosonization and modular transformations to theoretically study the phenomenon of superuniversality. Specifically, we introduce a new effective theory that has an emergent $U(N)$ gauge symmetry with any $N>1$ for a quantum phase transition between an integer quantum Hall state and an insulator. We then use modular transformations to generate from this theory effective descriptions for transitions between a large class of fractional quantum Hall states whose quasiparticle excitations have Abelian statistics. We find the correlation length and dynamical critical exponents are independent of the particular transition within a controlled 't Hooft large $N$ expansion, i.e., superuniversal! We argue that this superuniversality could survive away from this controlled large $N$ limit using recent duality conjectures.

4 pages, 2 figures, 6 pages of appendices; v2: new title, fixed typos and added various clarifications; v3: new intro and conclusion, various small edits

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• An all order exact result for the anomalous dimension of the scalar primary in Chern Simons Vector Models
• Collusion of Interactions and Disorder at the Superfluid-Insulator Transition: A Dirty 2d Quantum Critical Point
• Interaction effects on quantum Hall transitions: dynamical scaling laws and superuniversality
• Statistical interactions and boson-anyon duality in fractional quantum Hall fluids
• Emergent QCD${}_3$ Quantum Phase Transitions of Fractional Chern Insulators
• Fluctuations and magnetoresistance oscillations near the half-filled Landau level
• Delocalization and Universality of the Fractional Quantum Hall Plateau-to-Plateau Transitions
• Duality Web on a 3D Euclidean Lattice and Manifestation of Hidden Symmetries
• Non-Abelian Fermionization and the Landscape of Quantum Hall Phases
• Emergent reflection symmetry from non-relativistic composite fermions
• Continuous transition between Ising magnetic order and a chiral spin liquid
• A composite particle construction of the Fibonacci fractional quantum Hall state
• New and Old Fermionic Dualities from 3d Bosonization
• Composite Fermion Nonlinear Sigma Models
• Scaling and Diffusion of Dirac Composite Fermions
• Partial fillings of the bosonic $E_8$ quantum Hall state
• Weiss Oscillations in the Galilean-Invariant Dirac Composite Fermion Theory for Even-Denominator Filling Fractions of the Lowest Landau Level
• Random Magnetic Field and the Dirac Fermi Surface