Conformality loss and quantum criticality in topological Higgs electrodynamics in 2+1 dimensions

Abstract

The electromagnetic response of topological insulators and superconductors is governed by a modified set of Maxwell equations that derive from a topological Chern-Simons (CS) term in the effective Lagrangian with coupling constant κ. Here, we consider a topological superconductor or, equivalently, an Abelian Higgs model in 2+1 dimensions with a global O(2N) symmetry in the presence of a CS term, but without a Maxwell term. At large κ, the gauge field decouples from the complex scalar field, leading to a quantum critical behavior in the O(2N) universality class. When the Higgs field is massive, the universality class is still governed by the O(2N) fixed point. However, we show that the massless theory belongs to a completely different universality class, exhibiting an exotic critical behavior beyond the Landau-Ginzburg-Wilson paradigm. For finite κ above a certain critical value κc, a quantum critical behavior with continuously varying critical exponents arises. However, as a function κ, a transition takes place for |κ|κ 2 c, leading to the existence of a conformal fixed point, critical exponents are a function of κ.