Ferromagnetism in the strong hybridization regime of the periodic Anderson model

Abstract

We determine exactly the ground state of the one-dimensional periodic Anderson model (PAM) in the strong hybridization regime. In this regime, the low energy sector of the PAM maps into an effective Hamiltonian that has a ferromagnetic ground state for any electron density between half and three quarters filling. This rigorous result proves the existence of a new magnetic state that was excluded in the previous analysis of the mixed valence systems.Rigorous results, numerical and analytic, have greatly aided the study of strongly correlated electrons systems. Unfortunately, few such results exist. The numerical renormalization group and Bethe ansatz solutions of the single impurity Anderson and Kondo models are perhaps the best examples of a solid numerical approach and exact solution of simple models that changed and solidified the thinking in what was a highly controversial and puzzling problem area. Another important result was the rigorous connection between the two models established by Schrieffer and Wolff [1]. Their work showed that the low lying energy spectrum of the Anderson model in the strong coupling and weak hybridization limit (U/t ≫ 1 and V ≪ |E F −ǫ f |) can be mapped into the Kondo model in the weak coupling regime (J/t ≪ 1).For dense systems, the natural extensions of the impurity models are the periodic Anderson (PAM) and Kondo lattice (KLM) models. For these, numerical renormalization group and Bethe Ansatz solutions are lacking even in one-dimension. In addition, very few rigorous results are available for the PAM [2,3]. What remains true however is the connection between the strong and weak coupling limits via a natural extension of the Schrieffer-Wolff transformation.There are two basic questions one can ask about these lattice models: what is their relevance to real materials and in what other parameter regimes might their physics be connected? In several well known papers, Doniach [4], at least implicitly, made several assumptions about the answers to both questions and proposed the now standard picture of the magnetic properties of f-electron materials that portrays a competition between the RKKY magnetic interaction which is obtained from a fourth order expansion in the hybridization and the Kondo exchange.The reasoning behind this intuitively appealing picture is something like the following: From the Schrieffer-Wolff perturbation theory, the Kondo exchange coupling is related to the parameters in the PAM via J ≈ |V | 2 /|E F − ǫ f |. In the PAM, a mixed valence regime corresponds to positioning the f-electron orbitals in the conduction band near the Fermi energy, i.e., |E F − ǫ f | ≈ 0. In this regime, the Schrieffer-Wolff result suggests the Kondo exchange is strong and thus can lead to a complete compensation of the f-moments by one or more of the conduction band electrons. Implied in this line of reasoning there are two important assumptions [4]: I) The strong coupling limit of the KLM is connected to the mixed valence regime (for weak hybridzation |V | ≪ |t|) of the PAM, and II)...

Nuclear quantum effects on the high pressure melting of dense lithium

“…Our simulations were performed using the Vienna ab initio Simulation Package (VASP), with a self-developed combination of the TI and the ab initio MD/PIMD methods. 18,19,22 Perdew-Burke-Ernzerhof (PBE) functional within densityfunctional theory was used for descriptions of the electronic exchange-correlation interactions. Projector-augmented wave potentials (including 1s and 2s states as valence) were employed along with a 600 eV plane wave cutoff energy for the expansion of the Kohn-Sham orbitals.…”

“…A supercell containing 512 atoms was taken in the two-phase simulations, using Γ-point sampling, which gives a converged window of melting temperatures. 19,30 In the calculation of the free-energies, a 216-atom supercell was chosen, using a kmesh of 2 × 2 × 2. Thermal electronic excitations are handled using the standard methods of finite-temperature DFT developed by Mermin.…”

“…One approach which is often used nowadays consists of considering simultaneously the solid and liquid within the same box. 9,17,19 However, most studies along this direction are carried out using ab initio MD. The NQEs are absent.…”