O(4)-invariant formulation of the nodal liquid

Abstract

We consider the $O\left(4\right)\mathrm{}$ 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 $\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}\subset O\left(4\right)\mathrm{}$ symmetry is disordered by quantum fluctuations, the nodal liquid can result. In this context, we (1) construct a pseudospin σ model, (2) discuss its topological excitations, (3) point out the possibility of a pseudospin-Peierls state, and (4) propose a phase diagram for the underdoped cuprate superconductors.