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 → ∞), we were able to map out a phase diagram U vs 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 2, between a paramagnetic (PM) metal and a spin-density-wave (SDW) insulator; overall, the region U 2 corresponds to a PM metal for all n < 2. For 1 < n 1.5 a ferromagnetic phase is present within a range of U , while for 1.5 n < 2, 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.

Interorbital interaction in the one-dimensional periodic Anderson model: Density matrix renormalization group study

“…This analysis was later confirmed and refined by the density matrix renormalization group calculations [4][5][6]. Both methods showed that the charge gap is always larger than the spin gap, and decreases much more slowly than the spin gap as U f is increased and their ratio diverges in the large U f limit.…”

“…Namely, such large values of ξ can be explained with the known behavior of the ordinary PAM. As has been pointed out [5], the correlation length of the spin correlation function increases exponentially by increasing U f . As long as U cf is below the crossing point, the spin correlation function is dominant due to the tiny spin gap.…”

Spin-liquid state in an inhomogeneous periodic Anderson model

“…This means that around the middle of the trap, we have one atom at each site in both optical lattices, and they form a local singlet, establishing a spin liquid region for a global density ρ = 0.8; therefore, the charge redistribution generated by the harmonic potential and the transitions between the optical lattices stimulated by the local repulsion and the hybridization compete to reach a region with local singlets for this low global density. Note that the spin liquid phase for the well-known homogeneous periodic Anderson model can only be reached when the global density is ρ = 2 [31]. This means that harmonic potentials due to optical lattices open the door to obtaining spin liquid regions for different sets of parameters.…”

“…At quarter filling, a metal-insulator transition from a paramagnetic metal to an insulator with a localized-band spin-density wave was found. For incommensurate densities between a quarter and halffilling, the ground state is always metallic, but the magnetic behavior is quite diverse; for instance, we found paramagnetic, ferromagnetic, incommensurate spin density wave (ISDW), and RKKY regions [31].…”

“…facts about the two-orbital models is the spin liquid state, characterized by the formation of local singlets between carriers in different orbitals [24][25][26][27][28][29][30][31]. Taking into account the above, we decided to explore the formation of spin liquid regions inside of the trap as a function of the global density, the confining potential, the hybridization, and the local repulsion between the localized atoms.…”