Incommensurate spin-density-wave and metal-insulator transition in the one-dimensional periodic Anderson model

Abstract

We have used the density-matrix renormalization group method to study the ground-state properties of the symmetric periodic Anderson model in one dimension. We have considered lattices with up to ${N}_{s}=50$ sites, and electron densities ranging from quarter to half filling. Through the calculation of energies, correlation functions, and their structure factors, together with careful extrapolations (toward ${N}_{s}\ensuremath{\rightarrow}\ensuremath{\infty}$), we were able to map out a phase diagram $U\phantom{\rule{4pt}{0ex}}\mathrm{vs}\phantom{\rule{4pt}{0ex}}n$, where $U$ is the electronic repulsion on $f$ orbitals, and $n$ is the electronic density, for a fixed value of the hybridization. At quarter filling, $n=1$, our data is consistent with a transition at ${U}_{{c}_{1}}\ensuremath{\simeq}2$, between a paramagnetic (PM) metal and a spin-density-wave (SDW) insulator; overall, the region $U\ensuremath{\lesssim}2$ corresponds to a PM metal for all $nl2$. For $1ln\ensuremath{\lesssim}1.5$ a ferromagnetic phase is present within a range of $U$, while for $1.5\ensuremath{\lesssim}nl2$, we find an incommensurate SDW phase; above a certain ${U}_{c}(n)$, the system displays a Ruderman-Kittel-Kasuya-Yosida behavior, in which the magnetic wave vector is determined by the occupation of the conduction band. At half filling, the system is an insulating spin liquid, but with a crossover between weak and strong magnetic correlations.