Duality and Universality for the Chern-Simons bosons

Details Duality and Universality for the Chern-Simons bosons Duality and Universality for the Chern-Simons bosons

1995-11-30

arxiv.org/abs/cond-mat/9511140v2

Phys.Rev.B54:4953,1996

Physics

Condensed Matter

14 two-column pages, revtex 3.0, multicol and epsf.sty (optional), one PostScript figure, Submitted to Phys. Rev. B The change

Scientific paper

10.1103/PhysRevB.54.4953

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.

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