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On the high energy spin excitations in the high temperature superconductors: an RVB theory

The high energy spin excitation in the high T$_{c}$ cuprates is studied in the single mode approximation for the $t-t'-J$ model. An exact form for the mode dispersion is derived. When the Gutzwiller projected BCS state is used as the variational ground state, a spin-wave-like dispersion of about 2.2$J$ is uncovered along the $Γ=(0,0)$ to $\mathrm{M}=(π,0)$ line. Both the mode energy and the integrated intensity of the spin fluctuation spectrum are found to be almost doping independent in large doping range, which agrees very well with the observations of recent RIXS measurements. Together with previous studies on the quasiparticle properties of the Gutzwiiler projected BCS state, our results indicate that such a Fermionic RVB theory can provide a consistent description of both the itinerant and the local aspect of electronic excitations in the high T$_{c}$ cuprates.