The Kondo interaction coupling, Heisenberg exchange coupling, and Coulomb interactions within d-sites, were introduced in a one dimensional Periodic Anderson Model Hamiltonian (PAMH) to further investigate the effects of interaction parameters on the ground state energy of systems with heavy fermions (HF) behavior. Periodic Anderson model PAM being one of the most successful model for studying the heavy fermions System (HFS) was used in an extended version (mixed Kondo-Anderson representation) on a system of three-electrons interacting on three-sites cluster. Exact Diagonalization technique (EDT) normally used to solve conventional PAM calculation was considered in this work for a very small cluster. Hamiltonian used to describe this model contains the usual term describing the kinetic energy of the system, on-site coulomb repulsion and a hopping integral. The Hamiltonian is acted on the different Hilbert states of the lattice system and results of the interactions were obtained in terms of hopping integral, coulomb repulsions, exchange couplings and the hybridization term. Graphs of ground state energy Eo plotted agains tthese interaction parameters were presented in a clear format. As these parameters were varied numerically through a finite range of values, the individual effects of these parameters on the system’s ground state energy were observed and discussed. Hence, the results obtained from this work shows theoretically how the tuning of the Columbic interaction within the conduction band provides information that sheds light on the underlying physics of the heavy fermions systems models. Results obtained from this work further demonstrate the reliability of the model Hamiltonians that we have harnessed and the importance of considering electron-lattice interactions as well as interactions that account for magnetic impurities for the proper description of heavy fermions material.
The Kondo interaction coupling, Heisenberg exchange coupling, and Coulomb interactions within d-sites, were introduced in a one dimensional Periodic Anderson Model Hamiltonian (PAMH) to further investigate the effects of interaction parameters on the ground state energy of systems with heavy fermions (HF) behavior. Periodic Anderson model PAM being one of the most successful model for studying the heavy fermions System (HFS) was used in an extended version (mixed Kondo-Anderson representation) on a system of three-electrons interacting on three-sites cluster. Exact Diagonalization technique (EDT) normally used to solve conventional PAM calculation was considered in this work for a very small cluster. Hamiltonian used to describe this model contains the usual term describing the kinetic energy of the system, on-site coulomb repulsion and a hopping integral. The Hamiltonian is acted on the different Hilbert states of the lattice system and results of the interactions were obtained in terms of hopping integral, coulomb repulsions, exchange couplings and the hybridization term. Graphs of ground state energy Eo plotted agains tthese interaction parameters were presented in a clear format. As these parameters were varied numerically through a finite range of values, the individual effects of these parameters on the system’s ground state energy were observed and discussed. Hence, the results obtained from this work shows theoretically how the tuning of the Columbic interaction within the conduction band provides information that sheds light on the underlying physics of the heavy fermions systems models. Results obtained from this work further demonstrate the reliability of the model Hamiltonians that we have harnessed and the importance of considering electron-lattice interactions as well as interactions that account for magnetic impurities for the proper description of heavy fermions material.
The ground-state energy, wave-function, hybridization gap and magnetic phasediagram of the Single Site Impurity Anderson Model (SIAM) and the Periodic AndersonModel (PAM) were calculated using Exact-Diagonalization (ED) technique. The EDtechnique was applied to the SIAM and PAM in one dimension before speculating on Ce 4fbeing a test bed of the results, since it has 4f localized electrons in the Heavy fermioncompound CeCu2Si2. Each of the results obtained describe the evolution of the electronicsystem in terms of a simple set of parameters.The parameter regimes studied suggest asmooth phase transition from an antiferromagnetic (AFM) phase to a ferromagnetic (FM)phase at quarter fillings in one dimension when t increases and a magnetic instability wasobserved as U → ∞. The role of hybridization between the conduction electrons and thelocalized f orbital in the Anderson impurity in a semiconductor was also investigated as Vincreases in the SIAM and the PAM.
We investigate an extended version of the periodic Anderson model (the so-called periodic Anderson-Hubbard model) with the aim to understand the role of interaction between conduction electrons in the formation of the heavy-fermion and mixed-valence states. Two methods are used: (i) variational calculation with the Gutzwiller wave function optimizing numerically the ground-state energy and (ii) exact diagonalization of the Hamiltonian for short chains. The f-level occupancy and the renormalization factor of the quasiparticles are calculated as a function of the energy of the f orbital for a wide range of the interaction parameters. The results obtained by the two methods are in reasonably good agreement for the periodic Anderson model. The agreement is maintained even when the interaction between band electrons, Ud, is taken into account, except for the half-filled case. This discrepancy can be explained by the difference between the physics of the one- and higher-dimensional models. We find that this interaction shifts and widens the energy range of the bare f level, where heavy-fermion behavior can be observed. For large-enough Ud this range may lie even above the bare conduction band. The Gutzwiller method indicates a robust transition from Kondo insulator to Mott insulator in the half-filled model, while Ud enhances the quasiparticle mass when the filling is close to half filling.
Actinide- and Lanthanide based compounds are often considered as heavy Fermion (HF) systems. The essential ingredient for these systems is a localized d- or f-shell electron per lattice site which hybridizes with a non-interacting conduction band of p- or d-shell electrons. For temperatures below the so called coherence temperature Tc, the localized electrons stop to act like mag- netic scatterers known from the Kondo effect. There the conduction band electrons screen the local magnetic moments coherently. As a main effect the conduction electrons build a Fermi liquid (FL) of quasiparticles with strongly enhanced masses which exceed 10-1000 times the mass of the original electrons. These enhancements can be seen experimentally in an increased heat capacity coefficient and Pauli susceptibility. \nIn this work we employ the periodic Anderson model (PAM) to describe the paramagnetic phase of the heavy Fermion compounds. To solve the compli- cated many body problem the dynamical mean-field theory is adopted with the numerical renormalization group technique as impurity solver. \nWe find that for low conduction band fillings Tc decreases drastically, which is in accordance with the exhaustion effect predicted by Nozières [5]. Additionally we find, that the form of the free conduction band density of states is decisive to obtain a FL or a Mott insulating (MI) phase for strongly depleted conduction band fillings. \nFurthermore we investigate the PAM on a bipartite lattice, the coherence temperatures for each sublattice and especially the case of vanishing hybridiza- tion for one sublattice. In the latter case the system resembles a conduction band with only half the localized moment sites coupled to it. Our results show that it depends strongly on the chosen parameters if there is only one scale for the whole lattice or two distinct scales for each sublattice. Especially decoupling one sublattice leads to two separated scales. \nIn the last part the attention is focused on the two-impurity Anderson model and its solution via the DMFT method. We investigate the Anderson model and compare results to direct NRG calculations. Importantly, the two-impurity DMFT method can be easier extended to multi-impurity systems than the NRG on its own. This might lead to a method to efficiently examine multi- impurity systems.
The periodic Anderson model (PAM), where local electron orbitals interplay with itinerant electronic carriers, plays an essential role in our understanding of heavy fermion materials. Motivated by recent proposals for simulating the Kondo lattice model (KLM) in terms of alkaline-earth metal atoms, we take another step toward the simulation of PAM, which includes the crucial charge/valence fluctuation of local f-electrons beyond purely low-energy spin fluctuation in the KLM. To realize PAM, a transition induced by a suitable laser between the electronic excited and ground state of alkaline-earth metal atoms (1 S 0⇌3 P 0) is introduced. This leads to effective hybridization between local electrons and conduction electrons in PAM. Generally, the SU(N) version of PAM can be realized by our proposal, which gives a unique opportunity to detect large-N physics without complexity in realistic materials. In the present work, high-temperature physical features of standard [SU(2)] PAM with harmonic trapping potential are analyzed by quantum Monte Carlo and dynamic mean-field theory, where the Mott/orbital-selective Mott state was found to coexist with metallic states. Indications for near-future experiments are provided. We expect our theoretical proposal and (hopefully) forthcoming experiments will deepen our understanding of heavy fermion systems. At the same time, we hope these will trigger further studies on related Mott physics, quantum criticality, and non-trivial topology in both the inhomogeneous and nonequilibrium realms.
Continuous-time quantum Monte Carlo method combined with dynamical mean field theory is used to calculate both periodic Anderson model (PAM) and Kondo lattice model (KLM). Different parameter sets of both models are connected by the Schrieffer-Wolff transformation. For degeneracy N=2, a special particle-hole symmetric case of PAM at half filling which always fixes one electron per impurity site is compared with the results of the KLM. We find a good mapping between PAM and KLM in the limit of large on-site Hubbard interaction U for different properties like self-energy, quasiparticle residue and susceptibility. This allows us to extract quasiparticle mass renormalizations for the f electrons directly from KLM. The method is further applied to higher degenerate case and to realistic heavy fermion system CeRhIn5 in which the estimate of the Sommerfeld coefficient is proven to be close to the experimental value.
Various methods and approximation schemes are used to study many-electron interacting systems. Two important many-particle models, the Anderson model and the Hubbard model, and their electromagnetic properties have been investigated in many parameter regimes, and applied to physical systems. An Anderson single-impurity model Hamiltonian based calculation of the magnetic susceptibility is performed for YbN in the presence of crystal fields using an alteration of the Non-Crossing Approximation proposed by Zwicknagl et.al., incorporating parameters obtained from ab initio band structure calculations. It yields good agreement with experimental data. For the Anderson lattice model, a variational scheme which uses specific many-electron wavefunctions as basis is applied to both one- and two-dimensional systems represented by symmetric Anderson lattice Hamiltonians. Without much computational effort, the ground state energy is well approximated, especially in strong-coupling limit. Some electronic properties are examined using the variational ground state wavefunction. The one-dimensional Hubbard model has been solved exactly for small-size clusters by diagonalizing the Hamiltonian in the basis of many-electron Bloch states. The results for the energy spectrum and eigenfunctions of the ground state and low-lying excited states are presented. Also, mean field calculations of the two-dimensional single-band Hubbard model and Cu-O lattice model (three-band Hubbard model) are carried out for various physical quantities including the energy, occupation probability, staggered magnetization, momentum distribution Fermi surface and density of states, by using a projection operator formalism. To develop a systematic approach to solving many-electron problems, the many-particle partition function for the free electron gas system is explored using a cumulant expansion scheme. Starting from the ground state, the partition function can be approximated to any order in terms of excitation energy. Its application to interacting systems such as the Anderson model and the Hubbard model is briefly discussed.