Quantum Monte Carlo Simulations of the Half-Filled Two-Dimensional Kondo Lattice Model

The 2D half-filled Kondo lattice model with exchange $J$ and nearest neighbor hopping $t$ is considered. It is shown that this model belongs to a class of Hamiltonians for which zero-temperature auxiliary field Monte Carlo methods may be efficiently applied. We compute the staggered moment and spin and quasiparticle gaps on lattice sizes up to $12\times 12$. The competition between the RKKY interaction and Kondo effect leads to a continuous quantum phase transition between antiferromagnetic and spin-gapped insulators. This transition occurs at $J/t=1.45\mathrm{}\pm 0.05$.