Charge Order, Superconductivity, and a Global Phase Diagram of Doped Antiferromagnets

We investigate the interplay between lattice symmetry breaking and superconducting order in a two-dimensional model of doped antiferromagnets, with long-range Coulomb interactions and $\mathrm{Sp}\left(2N\right)$ spin symmetry, in the large- $N$ limit. Our results motivate the outline of a global phase diagram for the cuprate superconductors. We describe the quantum transitions between the phases, the evolution of their fermion excitation spectrum, and the experimental implications.