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

We present a detailed numerical study of ground state and finite temperature spin and charge dynamics of the two-dimensional Kondo lattice model with hopping t and exchange J. Our numerical results stem from auxiliary field quantum Monte Carlo simulations formulated in such a way that the sign problem is absent at half-band filling thus allowing us to reach lattice sizes up to $12\times 12.$ At $T=0\mathrm{}$ and antiferromagnetic couplings $J>\mathrm{}0\mathrm{}$ the competition between the Ruderman-Kittel-Kasuya-Yosida interaction and the Kondo effect triggers a quantum phase transition between antiferromagnetically ordered and magnetically disordered insulators: $J_c/t=1.45\mathrm{}\pm \mathrm{0.05.}$ At $J<\mathrm{}0\mathrm{}$ the system remains an antiferromagnetically ordered insulator and irrespective of the sign of J, the quasiparticle gap scales as $|J|.$ The dynamical spin structure factor $S(\overrightarrow{q},\omega )$ evolves smoothly from its strong-coupling form with spin gap at $\overrightarrow{q}=(\pi ,\pi )$ to a spin-wave form. For $J>\mathrm{}0,$ the single-particle spectral function $A(\overrightarrow{k},\omega )$ shows a dispersion relation following that of hybridized bands as obtained in the noninteracting periodic Anderson model. In the ordered phase this feature is supplemented by shadows, thus allowing an interpretation in terms of the coexistence of Kondo screening and magnetic ordering. In contrast, at $J<\mathrm{}0\mathrm{}$ the single-particle dispersion relation follows that of noninteracting electrons in a staggered external magnetic field. At finite temperatures spin $T_S$ and charge $T_C$ scales are defined by locating the maximum in the charge and spin uniform susceptibilities. For weak to intermediate couplings, $T_S$ marks the onset of antiferromagnetic fluctuations—as observed by a growth of the staggered spin susceptibility—and follows a $J^2$ law. At strong couplings $T_S$ scales as J. On the other hand $T_C$ scales as J both in the weak- and strong-coupling regime. At and slightly below $T_C$ we observe (i) the onset of screening of the magnetic impurities, (ii) a rise in the resistivity as a function of decreasing temperature, (iii) a dip in the integrated density of states at the Fermi energy, and finally (iv) the occurrence of hybridized bands in $A(\overrightarrow{k},\omega ).\mathrm{}$ It is shown that in the weak-coupling limit, the charge gap of order J is formed only at $T_S$ and is hence of magnetic origin. The specific heat shows a two-peak structure. The low-temperature peak follows $T_S$ and is hence of magnetic origin. Our results are compared to various mean-field theories.