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We present a detailed numerical study of spin and charge dynamics of thetwo-dimensional Kondo lattice model with hopping t and exchange J. At T=0 and J> 0, the competition between the RKKY interaction and Kondo effect triggers aquantum phase transition between magnetically ordered and disorderedinsulators: J_c/t = 1.45(5). The quasiparticle gap scales as |J|. S(q,\omega),evolves smoothly from its strong coupling form with spin gap at q = (\pi,\pi)to a spin wave form. At J>0, A(\vec{k},\omega) shows a dispersion relationfollowing that of hybridized bands. For J < J_c this feature is supplemented byshadows thus pointing to a coexistence of Kondo screening and magnetism. For J< 0 A(\vec{k},\omega) is similar to that of non-interacting electrons in astaggered magnetic field. Spin, T_S, and charge, T_C, scales are defined. Forweak to intermediate couplings, T_S marks the onset of antiferromagneticfluctuations and follows a J^2 law. At strong couplings T_S scales as J. T_Cscales as J both at weak and strong couplings. At and slightly below T_C weobserve i) a rise in the resistivity as a function of decreasing temperature,ii) a dip in the integrated density of states at the Fermi energy and iii) theoccurrence of hybridized bands in A(k,\omega). It is shown that in the weakcoupling limit, the charge gap of order J is of magnetic origin. The specificheat shows a two peak structure, the low temperature peak being of magneticorigin. Our results are compared to various mean-field theories.Comment: 30 pages, 24 figure

Spin and charge dynamics of the ferromagnetic and antiferromagnetic two-dimensional half-filled Kondo lattice model