Pseudogap Phase and the Quantum-Critical Point in Copper-Oxide Metals

A systematic solution of a model for copper oxides reveals a line of transitions ${T=T}_p\left(x\right)$ for $x$, the doping away from half filling less than a critical value, to a phase with broken time reversal and rotational symmetry. The single-particle spectrum in this phase is calculated to have a gap $\sim \left[\cos \right(k_{x}a/\pi )-\cos (k_{y}a/\pi ){]}^2$. The properties in this phase are compared to the properties of the so-called “pseudogap phase” of the copper oxides.