Quantum phase transition between integer quantum Hall states of bosons

2012/10/02 by Tarun Grover, Ashvin Vishwanath · 87 citations
Physics and Astronomy · #Boson #Condensed matter physics #Dirac fermion #Electron #Fermion #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum Hall effect #Quantum and electron transport phenomena #Quantum mechanics #Quantum phase transition #Quantum spin Hall effect #Superfluidity #Topological Materials and Phenomena #cond-mat.mes-hall #cond-mat.str-el #hep-th

paper · pdf · doi:10.1103/physrevb.87.045129

published in Physical Review B 87(4) (American Physical Society) · 11 pages, 3 figures

arxiv created 2012/10/02 · openalex publication_date 2013/01/31 · arxiv updated 2013/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Bosonic integer quantum Hall (IQH) phases are a class of symmetry-protected topological (SPT) phases that, similar to the fermionic IQH states, support a quantized Hall conductance. They, however, require interactions for their realization. Here, we study quantum Hall plateau transitions between a trivial insulator and a bosonic IQH phase, in a clean system. Generically, we find an intervening superfluid phase. The presence of additional symmetries, however, can potentially lead to a direct transition between these phases. We employ a fermionic parton description that captures both the insulating phases as well as the transition between them. The critical theory is massless QED-3 with N_f=2 fermion flavors. The fermions have a surprisingly simple interpretation: they are vortices of the superfluid. Therefore, the universal conductivity at the transition, assuming it is continuous, equals the universal resistivity of Dirac fermions in QED-3. We also briefly comment on sigma model descriptions of the transition and the surface states of related three-dimensional SPT phases.

Citations

• Large-Nestimates of universal amplitudes of theCPN−1theory and comparison with aS=12square-lattice model with competing four-spin interactions
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• Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State
• Percolation, quantum tunnelling and the integer Hall effect
• Deconfined Quantum Critical Points
• Putting competing orders in their place near the Mott transition

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