Universal collective modes from strong electronic correlations: Modified $1/{\mathcal{N}}_f$ theory with application to high-$T_c$ 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 semi-quantitative description of principal equilibrium properties of high-$T_c$ superconducting cuprates. The developed here scheme of 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, 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 non-monotonic 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 $t$-$J$-model approach to the charge dynamics in favor of more general $t$-$J$-$U$ and $t$-$J$-$U$-$V$ models. The results are also related to recent inelastic resonant $X$-ray and neutron scattering experiments for the high-$T_c$ cuprates.

References in corpus (15)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• Fate of the false Mott-Hubbard transition in two dimensions
• High-energy spin and charge excitations in electron-doped copper oxide superconductors
• The Fierz convergence criterion: a controlled approach to strongly-interacting systems with small embedded clusters
• Polarization resolved Cu $L_3$-edge resonant inelastic x-ray scattering of orbital and spin excitations in NdBa${}_2$Cu${}_3$O${}_{7-\delta }$
• Doping dependence of the magnetic excitations in La${}_{2-x}$Sr${}_x$CuO${}_4$
• Itinerant ferromagnetism in actinide 5f electrons system: Phenomenological analysis with spin fluctuation theory
• Crossover from Collective to Incoherent Spin Excitations in Superconducting Cuprates Probed by Detuned Resonant Inelastic X-ray Scattering
• High-energy magnetic excitations in overdoped La${}_{2-x}$Sr${}_x$CuO${}_4$ studied by neutron and resonant inelastic X-ray scattering
• Gutzwiller Magnetic Phase Diagram of the Cuprates
• Universal properties of high-temperature superconductors from real-space pairing III: The role of correlated hopping and intersite Coulomb interaction within the t-J-U model
• Numerically exploring the 1D-2D dimensional crossover on spin dynamics in the doped Hubbard model
• Charge Excitations in Nd${}_{2-x}$Ce${}_x$CuO${}_4$ Observed with Resonant Inelastic X-ray Scattering: Comparison of Cu K-edge with Cu L${}_3$-edge
• Charge-Density-Excitation Spectrum in the t-t'-J-V Model
• Interplay of charge and spin dynamics after an interaction quench in the Hubbard model