Schematic phase diagram of hole-doped cuprates (apart from those with La doping) as a function of temperature (T) and hole density (p). The antiferromagnetic (AF) insulator is present near <mml:math><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math>p=0, and the d-wave superconductor (dSC) is present below a critical temperature <mml:math><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math>Tc. The pseudogap (PG) is present for <mml:math><mml:mrow><mml:mi>T</mml:mi><mml:mo><</mml:mo><mml:msup><mml:mi>T</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:mrow></mml:math>T<T* and acquires density wave (DW) order at low T. The metallic states are the PG metal, the conventional Fermi liquid (FL), and the strange metal (SM). The dimer model of
the present paper describes only the PG metal as a fractionalized Fermi liquid (FL*).
