We consider the one-dimensional (1D) quasiperiodic Anderson-lattice model, which has quasiperiodically ordered impurities. The sites with an f-orbital are ordered as a “Fibonacci word”, one way to form 1D quasiperiodic orderings. To treat the correlation effect precisely, we use the density matrix renormalization group (DMRG) method. We show that the spin correlation function in the quasiperiodic system gives a characteristic pattern. Also, by analyzing the f-electron number and its fluctuation, we find that a valence transition, which usually occurs in the periodic Anderson model when the on-site interorbital interaction is large, is not sharp in the quasiperiodic system. Finally, we discuss the properties of the quasiperiodic Anderson-lattice model, comparing them against the Anderson-lattice model with randomly located f-orbitals. We find that the quasiperiodic Anderson-lattice model has a similar property to the periodic Anderson model for spin correlation, but also has a similar property to the Anderson-lattice model with randomly located f-orbitals for the valence fluctuation.
We investigate the effect of the Coulomb interaction,
Ucf, between the conduction and
f electrons in the periodic Anderson model using the density matrix renormalization group algorithm. We calculate the excitation spectrum of the half-filled symmetric model with an emphasis on the spin and charge excitations. In the one-dimensional version of the model, it is found that the spin gap is smaller than the charge gap below a certain value of
Ucf and the reversed inequality is valid for stronger
Ucf. This behavior is also verified by the behavior of the spin and density correlation functions. We also perform a quantum information analysis of the model and determine the entanglement map of the
f and conduction electrons. It is revealed that for a certain
Ucf the ground state is dominated by the configuration in which the conduction and
f electrons are strongly entangled, and the ground state is almost a product state. For larger
Ucf, the sites are occupied alternatingly dominantly by two
f electrons or by two conduction electrons.
We have studied the ground-state properties of the symmetric and asymmetric one-dimensional periodic Anderson model as a function of band filling and the model parameters
(V,U,and
Ef) using the local mean-field (LMF) approach. We have constructed the phase diagram for both cases and have calculated the energy, local moment, and occupation number of the f level. The LMF approach can reveal the basic properties of the system throughout the entire parameter space. For the symmetric case ${(E}_{f}=\ensuremath{-}U/2),$ close to quarter and half filling the antiferromagnetic phase is the ground state. For intermediate band-filling there is a second-order phase transition to a ferromagnetic state. At quarter filling there is a transition from a metallic paramagnetic state to an insulating antiferromagnetic state as the on-site Coulomb interaction increases. The asymmetric case is treated in the mixed-valence regime
(Ef=0). At half filling the ground state is antiferromagnetic while at or close to quarter filling it is paramagnetic. Below half filling the ground state becomes ferromagnetic, suggesting that doping destroys rapidly the antiferromagnetic $f\ensuremath{-}f$ spin correlations. For small values of U we find a paramagnetic state at all band fillings. Results for the average occupation number of the f level compare well with density matrix renormalization group calculations.
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
Ns=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
Uvsn, 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
n<2. For $1<n\ensuremath{\lesssim}1.5$ a ferromagnetic phase is present within a range of
U, while for $1.5\ensuremath{\lesssim}n<2$, we find an incommensurate SDW phase; above a certain
Uc(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.
Periodic Anderson model is one of the most important models in the field of strongly correlated electrons. With the recent developed numerical method density matrix embedding theory, we study the ground state properties of the periodic Anderson model on a two-dimensional square lattice. We systematically investigate the phase diagram away from half filling. We find three different phases in this region, which are distinguished by the local moment and the spin–spin correlation functions. The phase transition between the two antiferromagnetic phases is of first order. It is the so-called Lifshitz transition accompanied by a reconstruction of the Fermi surface. As the filling is close to half filling, there is no difference between the two antiferromagnetic phases. From the results of the spin–spin correlation, we find that the Kondo singlet is formed even in the antiferromagnetic phase.
We investigate the magnetic order and related strongly correlated effects in a one-dimensional Ising-Kondo lattice with transverse field. This model is the anisotropic limit of the conventional isotropic Kondo lattice model, in the sense that the itinerant electrons interact with the localized magnetic moments via only longitudinal Kondo exchange. Adopting the numerical density-matrix renormalization group method, we map out the ground-state phase diagram in various parameter spaces. Depending on the Kondo coupling and filling number, three distinct phases, including a metallic paramagnetic, a metallic ferromagnetic, and a gapped spin-density wave phase, are obtained. The spin-density wave is characterized by an ordering wave vector, which coincides with the nesting wave vector of the Fermi surface. This makes the corresponding magnetic transition a spin analog of the Peierls transition occurring in the one-dimensional metal. Moreover, by analyzing the momentum distribution function and charge correlation function, the conduction electrons are shown to behave like free spinless fermions in the ferromagnetic phase. We finally discuss the effect of the repulsive Hubbard interaction between conduction electrons. Our paper enriches the Kondo physics and deepens the current understanding of the heavy fermion compounds.
In order to better understand Kondo insulators, we have studied both the symmetric and asymmetric Anderson lattices at half filling in one dimension using the density-matrix formulation of the numerical renormalization group. The asymmetric case is treated in the mixed-valence regime. We have calculated the charge gap, the spin gap, and the quasiparticle gap as a function of the repulsive interaction U using open boundary conditions for lattices as large as 24 sites. We find that the charge gap is larger than the spin gap for all U for both the symmetric and asymmetric cases. Ruderman-Kittel-Kasuya-Yosida interactions are evident in the f-spin--f-spin correlation functions at large U in the symmetric case, but are suppressed in the asymmetric case as the f level approaches the Fermi energy. This suppression can also be seen in the staggered susceptibility \ensuremath{\chi}(q=2
kF) and it is consistent with neutron scattering measurements of \ensuremath{\chi}(q) in CeNiSn.