An Isotropic to Anisotropic Transition in a Fractional Quantum Hall State

Understand

We study a novel abelian gauge theory in 2+1 dimensions which has surprising theoretical and phenomenological features.

• The theory has a vanishing coefficient for the square of the electric field $e_i^2$, characteristic of a quantum critical point with dynamical critical exponent $z=2$, and a level-$k$ Chern-Simons coupling, which is {\it marginal} at this critical point.
• For $k=0$, this theory is dual to a free $z=2$ scalar field theory describing a quantum Lifshitz transition, but $k \neq 0$ renders the scalar description non-local.
• The $k \neq 0$ theory exhibits properties intermediate between the (topological) pure Chern-Simons theory and the scalar theory.