Self-Dual $\nu =1$ Bosonic Quantum Hall State in Mixed Dimensional QED

Abstract

We consider a (2+1) dimensional Wilson-Fisher boson coupled to a (3+1) dimensional U(1) gauge field. This theory possesses a strong-weak duality in terms of the coupling constant e, and is self-dual at a particular value of $e$. We derive exact relations between transport coefficients for a $\nu =1$ quantum Hall state at the self-dual point. Using boson-fermion duality, we map the $\nu =1$ bosonic quantum Hall state to a Fermi sea of the dual fermion, and observed that the exact relationships between transport coefficients at the bosonic self-dual point are reproduced by a simple random phase approximation, coupled with a Drude formula, in the fermionic theory. We explain this success of the RPA by pointing out a cancellation of a parity-breaking term in the fermion theory which occurs only at the self-dual point, resulting in the fermion self-dual theory explored previously. In addition, we argue n that the equivalence of self-dual structure can be understood in terms of electromagnetic duality or modular invariance, and these features are not inherited by the non-relativistic cousins of the present model.

arXiv comment9 pages, 1 figure

References in corpus (24)

• Quantum Phases of Vortices in Rotating Bose-Einstein Condensates
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Is the Composite Fermion a Dirac Particle?
• Deconfined quantum critical points: symmetries and dualities
• On Mirror Symmetry in Three Dimensional Abelian Gauge Theories
• Particle-Vortex Duality from 3d Bosonization
• Particle-vortex duality of 2d Dirac fermion from electric-magnetic duality of 3d topological insulators
• Ohm's Law at strong coupling: S duality and the cyclotron resonance
• Quantum Hall fractions in rotating Bose-Einstein condensates
• Dual Dirac liquid on the surface of the electron topological insulator
• Lowest-Landau-level theory of the quantum Hall effect: the Fermi-liquid-like state
• Quantum Electrodynamics of Particles on a Plane and the Chern-Simons Theory
• Duality between the deconfined quantum-critical point and the bosonic topological transition
• A dipole interpretation of the $\nu =1/2$ state
• Bosonization and Mirror Symmetry
• Nonsupersymmetric dualities from mirror symmetry
• Composite fermi liquids in the lowest Landau level
• Exact Boson-Fermion Duality on a 3D Euclidean Lattice
• Symmetry and duality in bosonization of two-dimensional Dirac fermions
• Duality and Universal Transport in a Mixed-Dimension Electrodynamics
• Holographic DC conductivity and Onsager relations
• Loop Models, Modular Invariance, and Three Dimensional Bosonization
• A series of (2+1)d Stable Self-Dual Interacting Conformal Field Theories
• Particle-vortex symmetric liquid

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