Duality and Universality for the Chern-Simons bosons

Abstract

By mapping the relativistic version of the Chern-Simons-Landau-Ginzburg theory in 2+1 dimensions to the 3D lattice Villain x-y model coupled with the Chern-Simons gauge field, we investigate phase transitions of Chern-Simons bosons in the limit of strong coupling. We construct algebraically exact duality and flux attachment transformations of the lattice theories, corresponding to analogous transformations in the continuum limit. These transformations are used to convert the model with arbitrary fractional Chern-Simons coefficient $\alpha$ to a model with $\alpha$ either zero or one. Depending on this final value of $\alpha$, the phase transition in the original model is either in the universality class of the 3D x-y model or a ``fermionic'' universality class, unless the irrelevant corrections of cubic and higher power in momenta render the transition of the first order.

14 two-column pages, revtex 3.0, multicol and epsf.sty (optional), one PostScript figure, Submitted to Phys. Rev. B The changes intended to simplify the arguments and eliminate logical gaps. We also show how the filling factor $\nu$ is changed by the duality transformation

References in corpus (5)

• Critical Exponents of the Superconducting Phase Transition
• Network Models of Quantum Percolation and Their Field-Theory Representations
• Fluctuation-Induced First Order Transition between the Quantum Hall Liquid and Insulator
• Equivalence of Several Chern-Simons Matter Models
• Spin Transmutation in (2+1) Dimensions

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• Quantum Hall Transition near a Fermion Feshbach Resonance in a Rotating Trap
• Reflection Symmetry and Quantized Hall Resistivity near Quantum Hall Transition
• Network of edge states: random Josephson junction array description
• Renormalization of modular invariant Coulomb gas and Sine-Gordon theories, and quantum Hall flow diagram
• Quantum Hall to Insulator Transition in the Bilayer Quantum Hall Ferromagnet
• Global symmetries of quantum Hall systems: lattice description
• Bilayer Quantum Hall Ferromagnet in a Periodic Potential
• Critical Behavior and Duality in Dimensionally Reduced Planar Chern-Simons Superconductors