Universal collective modes from strong electronic correlations: Modified 1/Nf theory with application to high- Tc cuprates

Abstract

A nonzero-temperature technique for strongly correlated electron lattice systems, combining elements of both variational wave function (VWF) approach and expansion in the inverse number of fermionic flavors ($1/{\mathcal{N}}_{f}$), is developed. The departure point, VWF method, goes beyond the renormalized mean-field theory and provides semiquantitative description of principal equilibrium properties of high-${T}_{c}$ superconducting cuprates. The developed here scheme of $\text{VWF}+1/{\mathcal{N}}_{f}$, in the leading order provides dynamical spin and charge responses around the VWF solution, generalizing the weak-coupling spin-fluctuation theory to the regime of strong correlations. Thermodynamic corrections to the correlated saddle-point state arise systematically at consecutive orders. Explicitly, $\text{VWF}+1/{\mathcal{N}}_{f}$ is applied to evaluate dynamical response functions for the hole-doped Hubbard model and compared with available determinant quantum Monte Carlo data, yielding a good overall agreement in the regime of coherent collective-mode dynamics. The emergence of well-defined spin and charge excitations from the incoherent continua is explicitly demonstrated and a nonmonotonic dependence of the charge-excitation energy on the interaction magnitude is found. The charge mode energy saturates slowly when approaching the strong-coupling limit, which calls for a reevaluation of the $t\text{\ensuremath{-}}J$-model approach to the charge dynamics in favor of more general $t\text{\ensuremath{-}}J\text{\ensuremath{-}}U$ and $t\text{\ensuremath{-}}J\text{\ensuremath{-}}U\text{\ensuremath{-}}V$ models. The results are also related to recent inelastic resonant x-ray and neutron-scattering experiments for the high-${T}_{c}$ cuprates.