Quantum Monte Carlo study of the one-dimensional symmetric Anderson lattice

Using a recently developed quantum Monte Carlo algorithm, we study the one-dimensional symmetric Anderson lattice. Through the use of boundary-condition averaging and imaginary-time increment extrapolation, we obtain controlled estimates for infinite-lattice properties, accurate to within a few percent, for a variety of parameters. Our results span high-temperature to, in some cases, ground-state properties. For U/Eg{}5, where U refers to the on-site Coulomb repulsion and Eg is the U=0 gap, we find spin correlations which decay quickly with distance in the ground state and a saturation temperature, at which quantities saturate to their ground-state values, which is independent of U. For U/Eg{}5, we find that nearby spin correlations decay more slowly with distance and saturation temperatures decrease with increasing U. For U/Eg{}8, we find that the nearby-spin-correlation development above the saturation temperature is well described by an Ruderman-Kittel-Kasuya-Yosida (RKKY) lattice effective Hamiltonian with perturbatively calculated parameters. We interpret this general behavior as a smooth crossover at U/Eg{~}5 from a basically noninteracting picture into a Kondo-lattice regime, parameterizable by RKKY interactions and a reduced effective gap. Next, using an exact canonical transformation, we point out what our results imply for superconductivity in an attractive-U Anderson lattice. Lastly, we discuss the relevance of our results to the magnetic behavior of heavy-fermion systems, which results underscore in particular the important role of RKKY interactions.