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.
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.
We study paramagnetic quantum criticality in the periodic Anderson model (PAM) using cellular dynamical mean-field theory (CDMFT), with the numerical renormalization group (NRG) as a cluster impurity solver. The PAM describes itinerant c electrons hybridizing with a lattice of localized f electrons. At zero temperature, it exhibits a much-studied quantum phase transition from a Kondo phase to a Ruderman-Kittel-Kasuya-Yosida (RKKY) phase when the hybridization is decreased through a so-called Kondo breakdown quantum critical point (KB QCP). There, Kondo screening of f spins by c electrons breaks down, so that f excitations change their character from somewhat itinerant to mainly localized, while c excitations remain itinerant. Building on , which interpreted the KB transition as an orbital-selective Mott transition, we here elucidate its nature in great detail by performing a high-resolution, real-frequency study of various dynamical quantities (susceptibilities, self-energies, and spectral functions). NRG allows us to study the quantum critical regime governed by the QCP and located between two temperature scales, T FL < T NFL . In this regime, we find fingerprints of non-Fermi-liquid (NFL) behavior in several dynamical susceptibilities. Surprisingly, CDMFT self-consistency is essential to stabilize the QCP and the NFL regime. The Fermi-liquid (FL) scale T FL decreases toward and vanishes at the KB QCP; at temperatures below T FL , FL behavior emerges. At T = 0 , we find the following properties. The KB transition is continuous. The f quasiparticle weight decreases continuously as the transition is approached from either side, vanishing only at the KB QCP. Therefore, the quasiparticle weight of the f band is nonzero not only in the Kondo phase, but also in the RKKY phase; hence, the FL quasiparticles comprise c f electrons in both phases. The Fermi surface (FS) volumes in the two phases differ, implying a FS reconstruction at the KB QCP. Whereas the large-FS Kondo phase has a two-band structure as expected, the small-FS RKKY phase unexpectedly has a three-band structure. We provide a detailed analysis of quasiparticle properties of both the Kondo and, for the first time, also the RKKY phase and uncover their differences. The FS reconstruction is accompanied by the appearance of a Luttinger surface on which the f self-energy diverges. The volumes of the Luttinger and Fermi surfaces are related to the charge density by a generalized Luttinger sum rule. We interpret the small FS volume and the emergent Luttinger surface as evidence for f -electron fractionalization in the RKKY phase. Finally, we compute the temperature dependence of the Hall coefficient and the specific heat, finding good qualitative agreement with experiments. Published by the American Physical Society 2024
The periodic Anderson model (PAM) is studied within the framework of dynamical mean-field theory, with particular emphasis on the interaction-driven Mott transition it contains, and on resultant Mott insulators of both Mott-Hubbard and charge-transfer type. The form of the PAM phase diagram is first deduced on general grounds using two exact results, over the full range of model parameters and including metallic, Mott, Kondo and band insulator phases. The effective low-energy model which describes the PAM in the vicinity of a Mott transition is then shown to be a one-band Hubbard model, with effective hoppings that are not in general solely nearest neighbour, but decay exponentially with distance. This mapping is shown to have a range of implications for the physics of the problem, from phase boundaries to single-particle dynamics; all of which are confirmed and supplemented by NRG calculations. Finally we consider the locally degenerate, non-Fermi liquid Mott insulator, to describe which requires a two-self-energy description. This is shown to yield a number of exact results for the associated local moment, charge, and interaction-renormalised levels, together with a generalisation of Luttinger's theorem to the Mott insulator.
Heavy-fermion or Kondo lattice materials are considered to be typical strongly correlated systems, for which mean-field approximations have shown that the Coulomb interaction increases the effective mass and narrows the band gap. In this paper, to clarify interaction effects on the electronic excitation, the spectral function of the Kondo lattice and periodic Anderson models is studied around Kondo insulators in the strong-coupling regime, by using the non-Abelian dynamical density-matrix renormalization group method and perturbation theory. Upon doping a Kondo insulator, an electronic mode emerges in the Kondo insulating gap, exhibiting the momentum-shifted magnetic dispersion relation. Although the ground-state properties are similar to those of a doped band insulator, the emergence of the electronic mode reflecting spin-charge separation of the Kondo insulator is a crucial interaction effect that allows us to regard the Kondo-insulator--metal transition as a type of Mott transition. In addition, electronic modes emerge even in the high-energy regime by doping in the periodic Anderson model. These strong-correlation effects have not been expected in conventional mean-field approximations and would bring a different perspective on heavy-fermion or Kondo lattice systems.
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.
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.
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.