  The pseudogap refers to an enigmatic state of matter with unusual physical
properties found below a characteristic temperature $T^*$ in hole-doped
high-temperature superconductors. Determining $T^*$ is critical for
understanding this state. Here we study the simplest model of correlated
electron systems, the Hubbard model, with cluster dynamical mean-field theory
to find out whether the pseudogap can occur solely because of strong coupling
physics and short nonlocal correlations. We find that the pseudogap
characteristic temperature $T^*$ is a sharp crossover between different
dynamical regimes along a line of thermodynamic anomalies that appears above a
first-order phase transition, the Widom line. The Widom line emanating from the
critical endpoint of a first-order transition is thus the organizing principle
for the pseudogap phase diagram of the cuprates. No additional broken symmetry
is necessary to explain the phenomenon. Broken symmetry states appear in the
pseudogap and not the other way around.
