Physics of the pseudogap phase of high Tc cuprates, or, RVB meets umklapp

It is argued that the dominant feature of the phase diagram of the high T_c cuprates is the crossover to the pseudogap phase in the energy (temperature) region E(T^∗). We argue that this scale is determined by the effective anti-ferromagnetic interaction which we calculate to be J_eff=J_{superexchange}−xt where x is the hole percentage and t the hopping integral.