Competing orders and quantum criticality in doped antiferromagnets

We use a number of large-N limits to explore the competition between ground states of square lattice doped antiferromagnets which break electromagneti c U(I), time-reversal,or square lattice space-group symmetries. Among the s tates we find are d-, (s* + id)-, and (d(x2+y2) + id(xy))-wave superconduct ors, Wigner crystals, Wigner crystals of hole pairs, orbital antiferromagne ts (or staggered-flux states), and states with spin-Peierls and bond-center ed charge stripe order. In the vicinity of second-order quantum phase trans itions between the states, we go beyond the large-N limit by identifying th e universal quantum field theories for the critical points, and computing t he finite temperature, quantum critical damping of fermion spectral functio ns. We identify candidate critical points for the recently observed quantum critical behavior in photoemission experiments on Bi2Sr2Ca Cu2O8+delta by Valla et al. [Science 285, 2110 (1999)]. These involve onset of a charge-de nsity wave, or of broken time-reversal symmetry with d(x2-y2) + id(xy) Or s * + id pairing, in a d-wave superconductor. Tt is not required (although it is allowed) that the stable state in the doped cuprates be anything other than the d-wave superconductor-the other states need only be stable nearby in parameter space. At finite temperatures, fluctuations associated with th ese nearby states lead to the observed fermion damping in the vicinity of t he nodal points in the Brillouin zone, The cases with broken time-reversal symmetry are appealing because the order parameter is not required to satis fy any special commensurability conditions. The observed absence of inelast ic damping of quasiparticles with moments (pi, k), (k, pi) (with 0 less tha n or equal to k less than or equal to pi) also appears very naturally for t he case of fluctuations to d(x2-y2) + id(xy) order.