Antiferromagnetic quantum phase transition in the quantum pseudogap phase of cuprates

We investigate a zero-temperature itinerant antiferromagnetic transition where the fermions possess a d-wave gap. This problem pertains to both the nodal liquid insulating phase and the d-wave superconducting phase of the underdoped cuprates. We find that a non-trivial quantum phase transition exists, and that the quantum critical point is dominated by a long-ranged interaction (|x - y|^-2d) of the Néel order parameter, which is induced by the Dirac-like fermions near gap nodes. We formulate a Ginzburg-Landau functional and estimate the critical exponents via the large-n expansion method.