2017/12/31 by Aaron Hui, Eun-Ah Kim, Michael Mulligan
Materials Science · Physics and Astronomy · #Bosonization #Condensed matter physics #Critical exponent #Electron #Graphene research and applications #Phase transition #Physics #Quantum Hall effect #Quantum and electron transport phenomena #Quantum mechanics #Quantum phase transition #Quantum spin Hall effect #Quasiparticle #Theoretical physics #Topological Materials and Phenomena #cond-mat.str-el #hep-th
paper · pdf · doi:10.1103/physrevb.99.125135
published as Phys. Rev. B 99, 125135 (2019) · 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
arxiv created 2019/03/20 · openalex publication_date 2019/03/20 · arxiv updated 2019/03/21 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/06
Quantum Hall inter-plateau 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.