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We explore the effect of local charge fluctuations on the spin response of aMott insulator by deriving an effective spin model, and studying it usingSchwinger boson mean field theory. Applying this to La$_2$CuO$_4$, we show thatan accurate fit to the magnon dispersion relation, measured by Coldea {\em etal.} [Phys. Rev. Lett. {\bf 86}, 5377 (2001)] is obtained with Hubbard modelparameters $U \approx 2.34 eV$, and $t \approx 360 meV$. These parameters leadto estimates of the staggered magnetization ($m_s \approx 0.25$), spin wavevelocity ($c\approx 800 meV$-\AA), and spin stiffness ($\rho_s \approx 24meV$). In particular the staggered moment as well as the effective local momentare renormalized to smaller values compared to the Heisenberg model due tolocal charge fluctuations in the Hubbard model. The dynamical structure factorshows considerable weight in the continuum along the zone boundary as well assecondary peaks that may be observed in high resolution neutron scatteringexperiments.Comment: Manuscript considerably revised following referee comments. Also  added a brief discussion of sum rules. 8 pages, 6 eps figure

physical review. b, condensed matter and materials physics

Effect of local charge fluctuations on spin dynamics in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">La</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mi mathvariant="normal">Cu</mml:mi><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:math>

Effect of local charge fluctuations on spin dynamics inLa2CuO4