Bond-operator theory of doped antiferromagnets: From Mott insulators with bond-centered charge order to superconductors with nodal fermions

The ground states and excitations of two-dimensional insulating and doped Mott insulators are described by a bond-operator formalism. While the method represents the degrees of freedom of an arbitrary antiferromagnet exactly, it is especially suited to systems in which there is a natural pairing of sites into bonds, as in states with spontaneous or explicit spin-Peierls order (or bond-centered charge order). In the undoped insulator, as discussed previously, we obtain both paramagnetic and magnetically ordered states. We describe the evolution of superconducting order in the ground state with increasing doping—at low doping, the superconductivity is weak, can coexist with magnetic order, and there are no gapless spin-1/2 fermionic excitations; at high doping, the magnetic order is absent and we obtain a BCS d-wave superconductor with gapless spin-1/2 nodal fermions. We present the critical theory describing the onset of these nodal fermionic excitations. We discuss the evolution of the spin spectrum and obtain regimes where a spin-1 exciton contributes a sharp resonance in the dynamic spin susceptibility. We also discuss the experimental consequences of low-energy, dynamically fluctuating spin-Peierls order in an isotropic ${\mathrm{CuO}}_2$ plane—we compute consequences for the damping and dispersion of an optical phonon involving primarily the O ions and compare the results with recent neutron scattering measurements of phonon spectra.