One-dimensional Anderson Lattice Research Articles

Coexistence of extended and localized states in the one-dimensional non-Hermitian Anderson model

In one-dimensional Hermitian tight-binding models, mobility edges separating extended and localized states can appear in the presence of properly engineered quasi-periodical potentials and coupling constants. On the other hand, mobility edges don't exist in a one-dimensional Anderson lattice since localization occurs whenever a diagonal disorder through random numbers is introduced. Here, we consider a nonreciprocal non-Hermitian lattice and show that the coexistence of extended and localized states appears with or without diagonal disorder in the topologically nontrivial region. We discuss that the mobility edges appear basically due to the boundary condition sensitivity of the nonreciprocal non-Hermitian lattice.

Double-exchange mechanism in rare-earth compounds

We show that double-exchange mechanism is responsible for ferromagnetism in low dimensional rare-earth compounds. We use the bosonized version of the one-dimensional Anderson lattice model in Toulouse limit to characterize the properties of the emerging ferromagnetic phase. We give a comprehensive description of the ferromagnetic ordering of the correlated electrons which appears at intermediate couplings and doping. The obtained ferromagnetic phase transitions have been identified to be an order–disorder transition of the quantum random transverse-field Ising type.

Ordering of correlated electrons in rare-earth compounds

We show that the correlated electrons in low dimensional rare-earth compounds give rise to a ferromagnetic phase. We use a bosonized version of the one-dimensional Anderson lattice model in Toulouse limit to characterize the properties of this emerging ferromagnetism. We show that ferromagnetism originates from a double-exchange mechanism. We obtain two transitions into a ferromagnetic phase, both are quantum order–disorder transitions of the quantum transverse-field Ising type. This reflects double-exchange ordered regions of correlated spins being gradually destroyed as the coupling to the conduction electrons is reduced. For incommensurate conduction-band filling, the low-energy properties of the correlated spins near the transition are dominated by anomalous ordered (disordered) regions of correlated spins, which survive into the paramagnetic (ferromagnetic) phase. We give a comprehensive description of the emerging ferromagnetic phase and determine the critical properties of the phase transitions.

Ferromagnetic order in the one-dimensional Anderson lattice

Using bosonization an effective Hamiltonian is derived for the one-dimensional Anderson lattice model in the Toulouse limit. The effective Hamiltonian exhibits ferromagnetic ground state in the intermediate coupling regime. • 1D Anderson lattice is bosonized in the Toulouse limit. • The obtained effective Hamiltonian exhibits ferromagnetic order. • Ferromagnetism is due to a double-exchange mechanism. • The ferromagnetic transition has been identified to be an order–disorder transition.

Magnetism in rare-earth alloys

Low dimensional rare-earth alloys reveal a rich phase diagram which always incorporate a ferromagnetic (FM) phase. Here we show that rare-earth ferromagnetism in low dimensions is due to double-exchange mechanism. We use the bosonized version of the one-dimensional Anderson lattice model in Toulouse limit to characterize the properties of this emerging FM phase. We give a comprehensive description of the FM ordering of the correlated electrons which appears at intermediate couplings and doping. Determine the critical properties of the phase transitions into the quantum disordered paramagnetic phases. The obtained phase transitions have been identified to be an order–disorder transition of the quantum random transverse-field Ising type.

Non-local correlations in the one-dimensional Anderson lattice

An effective Hamiltonian is derived via bosonization for the one-dimensional Anderson lattice model in the Toulouse limit. The effective Hamiltonian exhibits ferromagnetic ground state in the intermediate coupling regime.

Zero Energy Anomaly in One-Dimensional Anderson Lattice with Exponentially Correlated Weak Diagonal Disorder

We calculated numerically the localization length of one-dimensional Anderson model with correlated diagonal disorder. For zero energy point in the weak disorder limit, we showed that the localization length changes continuously as the correlation of the disorder increases. We found that higher order terms of the correlation must be included into the current perturbation result in order to give the correct localization length, and to connect smoothly the anomaly at zero correlation with the perturbation result for large correlation.

Variational Monte Carlo Study of Flat Band Ferromagnetism –Application to CeRh3B2–

A new mechanism for ferromagnetism in CeRh_3B_2 is proposed on the basis of variational Monte Carlo results. In a one-dimensional Anderson lattice where each 4f electron hybridizes with a ligand orbital between neighboring Ce sites, ferromagnetism is stabilized due to a nearly flat band which is a mixture of conduction and 4f electron states. Because of the strong spin-orbit interaction in 4f electron states, and of considerable amount of hybridization in the nearly flat band, the magnetic moments from 4f and conduction electrons tend to cancel each other. The resultant ferromagnetic moment becomes smaller as compared with the local 4f moment, and the Fermi surface in the ferromagnetic ground state is hardly affected by the presence of 4f electrons. These theoretical results are consistent with experimental observations in CeRh_3B_2 by neutron scattering and dHvA effects.

Phase diagram of the one-dimensional periodic Anderson model

We have calculated the phase diagram of the symmetric one-dimensional Anderson lattice using the local mean-field method, which can reveal the basic properties of the system throughout the entire parameter space. Near quarter and half filling the antiferromagnetic phase is the ground state. For intermediate band filling there is a continuous 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.

Disorder effects in the one-dimensional Anderson lattice model

We have studied the one-dimensional periodic, symmetric Anderson model at half filling in the presence of disorder using finite-temperature quantum Monte Carlo techniques. We have considered the disorder of both the hybridization between the local f-orbitals and the conduction electrons and the local f-site energy, using a uniform distribution of width Δ. The f-orbital local magnetic moment, the static magnetic susceptibility, the charge susceptibility, and the nearest-neighber magnetic correlation function have been calculated as a function of the disorder distribution width Δ. We find that the hybridization disorder has a dramatical effect on the low-temperature magnetic properties giving rise to a non-Fermi liquid behavior, and that the magnetic susceptibility can be scaled by a power law with an exponent which is in excellent agreement with experiment. On the other hand, disorder of the local f-orbital energy level does not show a non-Fermi liquid behavior.

Effect of dispersion in the f band of the one-dimensional Anderson lattice model.

We study the effect of a small dispersion in the f band on the elementary excitations of the one-dimensional Anderson lattice at half filling. We use the density-matrix renormalization-group technique to study the strong-coupling case (large Coulomb repulsion U) and an analytic renormalization-group calculation for weak coupling. When U=0, even a small dispersion in the f band can close the hybridization gap. In contrast, when U is large, the quasiparticle gap remains open and is almost independent of the dispersion in the f band. This means that for a given value of the dispersion, there is a metal-insulator transition for some value of the Coulomb repulsion U. The analytic calculation shows that the transition occurs at U=0. In contrast to the quasiparticle gap, the spin gap is strongly suppressed by the dispersion in the f band. This suppression is associated with the enhancement of antiferromagnetic correlations. \textcopyright{} 1996 The American Physical Society.

Phase diagram of the one-dimensional Anderson lattice.

We map out the phase diagram of the one--dimensional Anderson lattice by studying the ground state magnetization as a function of band--filling using the density matrix renormalization group technique. For strong coupling, we find that the quarter--filled system has an S=0 ground state with strong antiferromagnetic correlations. As additional electrons are put in, we find first a ferromagnetic phase, as reported by M\"{o}ller and W\"{o}lfle, and then a phase in which the ground state has total spin $S=0$. Within this $S=0$ phase, we find RKKY oscillations in the spin--spin correlation functions.

Heavy quasiparticles in the Anderson lattice model.

An exact-diagonalization technique on small clusters is used to study the dynamics of the one-dimensional symmetric Anderson lattice model. Our calculated excitation spectra reproduce key features expected for an infinite Kondo lattice such as nearly localized low-energy spin excitations and extended regions of ``heavy-quasiparticle'' bands. We show that, in contrast to the hybridization picture, low-energy spin excitations of the nearly localized $f$-electron system play a key role in the formation of an almost dispersionless low-energy band of heavy quasiparticles.

Influence of electron-phonon interaction to the periodic Anderson lattice

In heavy fermion compounds, the hybridization effect between the conduction and localized f-orbital electrons gives rise to a breathing phonon mode. This breathing mode couples with the conduction electrons and renormalizes the conduction bandwidth. Using the perturbation method for the one-dimensional periodic Anderson lattice, we study the influence of electron-phonon coupling on the hybridization effect and the stability of paramagnetic and antiferromagnetic states. Our results show that both the hybridization effect and Kondo temperature are reduced. This effect is more significant at large hybridization interaction in that it will destroy the stability of the antiferromagnetic state. However, this is already beyond the parameter ranges for the heavy fermion compounds.

Kondo insulators modeled by the one-dimensional Anderson lattice: A numerical-renormalization-group study

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. We have calculated the charge gap, spin gap and 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. RKKY 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 and it is consistent with neutron scattering measurements in CeNiSn.

Numerical renormalization group study of the one-dimensional Anderson lattice

We have studied both the symmetric and asymmetric period. Anderson model in one dimension using the density matrix formulation of the numerical renormalization group. We have calculated the charge gap, spin gap and quasiparticle gap as a function of the repulsive interaction U using open boundary conditions for lattices up to 24 sites at half filling. We find that the charge gap is larger than the spin gap for all U for both the symmetric and asymmetric cases.

Many-electron variational calculation for the one-dimensional Anderson lattice.

We present a variational method for studying the ground-state properties of the one-dimensional Anderson model with periodic boundary conditions. Our results are compared with exact Monte Carlo results and show excellent agreement in the large-U limit. We argue that poor results in the vanishing-U range are due to the truncated basis chosen, as well as the fact that all fluctuations are treated equally.

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/${E}_{g}$\ensuremath{\lesssim}5, where U refers to the on-site Coulomb repulsion and ${E}_{g}$ 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/${E}_{g}$\ensuremath{\gtrsim}5, we find that nearby spin correlations decay more slowly with distance and saturation temperatures decrease with increasing U. For U/${E}_{g}$\ensuremath{\gtrsim}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/${E}_{g}$\ensuremath{\sim}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.

Spin- and charge-density-wave instabilities in heavy-fermion systems

Spin- and charge-density-wave (SDW, CSW) instabilities are formulated starting from the one-dimensional Anderson lattice model by deriving microscopic gap equations. In the infinite-U case, the author shows that SDW phase does not appear but CSW may occur. The reason for this difference is that the physical meaning of the slave-boson fluctuation is the fluctuation of charge. In order to incorporate spin fluctuations, application of the 'finite-U' slave-boson technique is proposed. Qualitative features of SDW phase described by the second-order gap equation are discussed.

Perturbation theory of the one-dimensional Anderson lattice

The ground-state densities of states and single-particle dispersions of the one-dimensional periodic Anderson Hamiltonian with Coulomb screening U s are studied by perturbation expansion in U and U s for the half-filled ( N e/ N = 2) symmetric case.