O(4)-Invariant Formulation of the Nodal Liquid

Abstract

We consider the O(4) symmetric point in the phase diagram of an electron system in which there is a transition between d_{x^2 - y^2} density-wave order and d_{x^2 - y^2} superconductivity. If the pseudospin $SU(2)\subset O(4)$ symmetry is disordered by quantum fluctuations, the Nodal Liquid can result. In this context, we (1) construct a pseudospin $\sigma$-model; (2) discuss its topological excitations; (3) point out the possibility of a {\it pseudospin-Peierls} state and (4) propose a phase diagram for the underdoped cuprate superconductors.