Periodic Anderson Model Research Articles

Principal component analysis for fermionic critical points

We use determinant Quantum Monte Carlo (DQMC), in combination with the principal component analysis (PCA) approach to unsupervised learning, to extract information about phase transitions in several of the most fundamental Hamiltonians describing strongly correlated materials. We first explore the zero temperature antiferromagnet to singlet transition in the Periodic Anderson Model, the Mott insulating transition in the Hubbard model on a honeycomb lattice, and the magnetic transition in the 1/6-filled Lieb lattice. We then discuss the prospects for learning finite temperature superconducting transitions in the attractive Hubbard model, for which there is no sign problem. Finally, we investigate finite temperature charge density wave (CDW) transitions in the Holstein model, where the electrons are coupled to phonon degrees of freedom, and carry out a finite size scaling analysis to determine $T_c$. We examine the different behaviors associated with Hubbard-Stratonovich auxiliary field configurations on both the entire space-time lattice and on a single imaginary time slice, or other quantities, such as equal-time Green's and pair-pair correlation functions.

Matching DMFT calculations with photoemission spectra of heavy fermion insulators: universal properties of the near-gap spectra of SmB6

Paramagnetic heavy fermion insulators consist of fully occupied quasiparticle bands inherent to Fermi liquid theory. The gap emergence below a characteristic temperature is the ultimate sign of coherence for a many-body system, which in addition can induce a non-trivial band topology. Here, we demonstrate a simple and efficient method to compare a model study and an experimental result for heavy fermion insulators. The temperature dependence of the gap formation in both local moment and mixed valence regimes is captured within the dynamical mean field (DMFT) approximation to the periodic Anderson model (PAM). Using the topological coherence temperature as the scaling factor and choosing the input parameter set within the mixed valence regime, we can unambiguously link the theoretical energy scales to the experimental ones. As a particularly important result, we find improved consistency between the scaled DMFT density of states and the photoemission near-gap spectra of samarium hexaboride (SmB6).

Laser-irradiated Kondo insulators: Controlling the Kondo effect and topological phases

We theoretically investigate the nature of laser-irradiated Kondo insulators. Using Floquet theory and slave boson approach, we study a periodic Anderson model and derive an effective model which describes the laser-irradiated Kondo insulators. In this model, we find two generic effects induced by laser light. One is the dynamical localization, which suppresses hopping and hybridization. The other is the laser-induced hopping and hybridization, which can be interpreted as a synthetic spin-orbit coupling or magnetic field. The first effect drastically changes the behavior of the Kondo effect. Especially, the Kondo effect under laser light qualitatively changes its character depending on whether the hybridization is on-site or off-site. The second effect triggers topological phase transitions. In topological Kondo insulators, linearly polarized laser light realizes phase transitions between trivial, weak topological, and strong topological Kondo insulators. Moreover, circularly polarized laser light breaks time-reversal symmetry and induces Weyl semimetallic phases. Our results pave the new way to dynamically control the Kondo effect and topological phases in heavy fermion systems. We also discuss experimental setups to detect the signatures.

Topological phase in 1D topological Kondo insulator: Z2 topological insulator, Haldane-like phase and Kondo breakdown

We have simulated a half-filled $1D$ $p$-wave periodic Anderson model with numerically exact projector quantum Monte Carlo technique, and the system is indeed located in the Haldane-like state as detected in previous works on the $p$-wave Kondo lattice model, though the soluble non-interacting limit corresponds to the conventional $Z_{2}$ topological insulator. The site-resolved magnetization in an open boundary system and strange correlator for the periodic boundary have been used to identify the mentioned topological states. Interestingly, the edge magnetization in the Haldane-like state is not saturated to unit magnetic moment due to the intrinsic charge fluctuation in our periodic Anderson-like model, which is beyond the description of the Kondo lattice-like model in existing literature. The finding here underlies the correlation driven topological state in this prototypical interacting topological state of matter and naive use of non-interacting picture should be taken care. Moreover, no trace of the surface Kondo breakdown at zero temperature is observed and it is suspected that frustration-like interaction may be crucial in inducing such radical destruction of Kondo screening. The findings here may be relevant to our understanding of interacting topological materials like topological Kondo insulator candidate SmB$_{6}$.

The role of short-range magnetic correlations in the gap opening of topological Kondo insulators

In this article we investigate the effects of short-range anti-ferromagnetic correlations on the gap opening of topological Kondo insulators. We add a Heisenberg term to the periodic Anderson model at the limit of strong correlations in order to allow a small degree of hopping of the localized electrons between neighboring sites of the lattice. This new model is adequate for studying topological Kondo insulators, whose paradigmatic material is the compound . The main finding of the article is that the short-range antiferromagnetic correlations, present in some Kondo insulators, contribute decisively to the opening of the Kondo gap in their density of states. These correlations are produced by the interaction between moments on the neighboring sites of the lattice.For simplicity, we solve the problem on a two dimensional square lattice. The starting point of the model is the ions orbitals, with multiplet in the presence of spin–orbit coupling. We present results for the Kondo and for the antiferromagnetic correlation functions. We calculate the phase diagram of the model, and as we vary the level position from the empty regime to the Kondo regime, the system develops metallic and topological Kondo insulator phases. The band structure calculated shows that the model describes a strong topological insulator.

Universal scaling in the Knight-shift anomaly of the doped periodic Anderson model

We report a Dynamical Cluster Approximation (DCA) investigation of the doped periodic Anderson model (PAM) to explain the universal scaling in the Knight shift anomaly predicted by the phenomenological two-fluid model and confirmed in many heavy-fermion compounds. We calculate the quantitative evolution of the orbital-dependent magnetic susceptibility and reproduce correctly the two-fluid prediction in a large range of doping and hybridization. Our results confirm the presence of a temperature/energy scale $T^{\ast}$ for the universal scaling and show distinctive behavors of the Knight shift anomaly in response to other "orders" at low temperatures. However, comparison with the temperature evolution of the calculated resistivity and quasiparticle spectral peak indicates a different characteristic temperature from $T^*$, in contradiction with the experimental observation in CeCoIn$_5$ and other compounds. This reveals a missing piece in the current model calculations in explaining the two-fluid phenomenology.

Effects of an additional conduction band on the singlet-antiferromagnet competition in the periodic Anderson model

The competition between antiferromagnetic (AF) order and singlet formation is a central phenomenon of the Kondo and Periodic Anderson Hamiltonians, and of the heavy fermion materials they describe. In this paper, we explore the effects of an additional conduction band on magnetism in these models, and, specifically, on changes in the AF-singlet quantum critical point (QCP) and the one particle and spin spectral functions. To understand the magnetic phase transition qualitatively, we first carry out a self-consistent mean field theory (MFT). The basic conclusion is that, at half-filling, the coupling to the additional band stabilizes the AF phase to larger $f$ $d$ hybridization $V$ in the PAM. We also explore the possibility of competing ferromagnetic phases when this conduction band is doped away from half-filling. We next employ Quantum Monte Carlo (QMC) which, in combination with finite size scaling, allows us to evaluate the position of the QCP using an exact treatment of the interactions. This approach confirms the stabilization of AF order, which occurs through an enhancement of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. QMC results for the spectral function $A(\textbf{q},\omega)$ and dynamic spin structure factor $\chi(\textbf{q},\omega)$ yield additional insight into the AF-singlet competition and the low temperature phases.

Insight into the temperature dependent properties of the ferromagnetic Kondo lattice YbNiSn

Analyzing temperature dependent photoemission (PE) data of the ferromagnetic Kondo-lattice (KL) system YbNiSn in the light of the Periodic Anderson model (PAM) we show that the KL behavior is not limited to temperatures below a temperature T_K, defined empirically from resistivity and specificic heat measurements. As characteristic for weakly hybridized Ce and Yb systems, the PE spectra reveal a 4f-derived Fermi level peak, which reflects contributions from the Kondo resonance and its crystal electric field (CEF) satellites. In YbNiSn this peak has an unusual temperature dependence: With decreasing temperature a steady linear increase of intensity is observed which extends over a large interval ranging from 100 K down to 1 K without showing any peculiarities in the region of T_K ~ TC= 5.6 K. In the light of the single-impurity Anderson model (SIAM) this intensity variation reflects a linear increase of 4f occupancy with decreasing temperature, indicating an onset of Kondo screening at temperatures above 100 K. Within the PAM this phenomenon could be described by a non-Fermi liquid like T- linear damping of the self-energy which accounts phenomenologically for the feedback from the closely spaced CEF-states.

Simulating heavy fermion physics in optical lattice: Periodic Anderson model with harmonic trapping potential

Periodic Anderson model (PAM), where local electron orbitals interplay with itinerant electronic carriers, plays an essential role in our understanding on heavy fermion materials. Motivated by recent proposal of simulating Kondo lattice model (KLM) in terms of alkaline-earth metal atoms, we make a further step toward simulation of PAM, which includes crucial charge/valence fluctuation of local f-electron beyond purely low-energy spin fluctuation in KLM. To realize PAM, transition induced by suitable laser between electronic excited and ground state of alkaline-earth metal atoms ($^{1}S_{0}$$\rightleftharpoons$$^{3}P_{0}$) is introduced, and it leads to effective hybridization between local electron and conduction electron 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 feature of standard ($SU(2)$) PAM with harmonic trapping potential is detailed analyzed by quantum Monte Carlo and dynamic mean-field theory. Indications for near-future experiments are provided. We expect our theoretical proposal and (hopefully) forthcoming experiment will deepen our understanding on heavy fermion systems and at the same time triggers further studies on related Mott physics, quantum criticality and non-trivial topology in both inhomogeneous and nonequilibrium realm.

Phonon response of some heavy Fermion systems in dynamic limit

The phonon excitation spectrum of some Heavy Fermion (HF) systems in the presence of electron–phonon interaction is studied in the dynamic limit ([Formula: see text]). The renormalized excitation phonon frequencies ([Formula: see text]) are evaluated through Periodic Anderson Model (PAM) in the presence of electron–phonon interaction using Zubarev-type double time temperature-dependent Green function. The calculated renormalized phonon energy is analyzed through the plots of ([Formula: see text]) against temperature for different system parameters like effective coupling strength ‘[Formula: see text]’ and the position of [Formula: see text]-level ‘[Formula: see text]’. The observed behavior is analyzed and found to agree with the general features of HF systems found in experiments. Further, it is observed that in finite but small [Formula: see text]-values the propagating phonons harden and change to localized peaks.

Doping-induced perturbation and percolation in the two-dimensional Anderson lattice

We examine the doping effects in the two-dimensional periodic Anderson model using the determinant Quantum Monte Carlo (DQMC) method. We observe bound states around the Kondo hole site and find that the heavy electron states are destroyed at the nearest-neighbor sites. Our results show no clear sign of hybridization oscillation predicted in previous mean-field calculations. We further study the electron transport with increasing doping and as a function of temperature and obtain a critical doping xc ≈ 0.6 that marks a transition from the Kondo insulator regime to the single-ion Kondo regime. The value of xc is in good agreement with the predicted threshold for the site percolation. Our results confirm the percolative nature of the insulator-metal transition widely observed in doped Kondo insulators.

Mott transitions with partially filled correlated orbitals

We investigate the metal-insulator Mott transition in a generalized version of the periodic Anderson model, in which a band of itinerant non-interacting electrons is hybridrized with a narrow and strongly correlated band. Using the dynamical mean-field theory, we show that the precondition for the Mott transition is that the total filling of the two bands takes an odd integer value. Unlike the conventional portrait of the Mott transition, this condition corresponds to a non-integer filling of the correlated band. For an integer constant occupation of the correlated orbitals the system remains a correlated metal at arbitrary large interaction strength. We picture the transition at a non-integer filling of the correlated orbital as the Mott localization of the singlet states between itinerant and strongly interacting electrons, having occupation of one per lattice site. We show that the Mott transition is of the first order and we characterize the nature of the resulting insulating state with respect to relevant physical parameters, such as the charge-transfer energy.

Observation of the c‐f hybridization effect in valence‐transition system EuPtP

We study the electronic structure of EuPtP, which exhibits two first‐order valence transitions at T1 = 247 K and T2 = 201 K, using angle‐resolved photoemission spectroscopy. Below T2, we observe an energy gap at the crossing point of the bulk Eu 4f and conduction bands. The shape of band dispersions is described by a hybridization‐band picture based on the periodic Anderson model. Our results demonstrate the c‐f hybridization effect in the low‐temperature phase of EuPtP.

Manifestation of spin-charge fluctuations in the spectral and thermodynamic properties of quasi-two-dimensional rare-earth intermetallic compounds

In the framework of the modified periodic Anderson model with exchange interaction in the subsystem of localized states, it is shown that spin-charge fluctuations in quasi-two-dimensional intermetallic compounds with rare-earth ions in the mixed valence state significantly affect both the spectrum of magnetic excitations and the conditions at which the antiferromagnetic phase is realized. The spectral characteristics of the phase were obtained by the method of the diagram technique for Hubbard operators in the one-loop approximation, which allows to account for the spin-charge fluctuation contributions to the components of the mass and the force operators. The developed theory allowed to quantitatively describe the pressure dependence of the Neel temperature observed in a quasi-two-dimensional antiferromagnetic heavy-fermion intermetallic compound CeRhIn5.

The c–f hybridization effect in the subsurface region of YbInCu4

We studied the electronic structure of YbInCu4, which exhibits a first-order valence transition, using angle-resolved photoemission spectroscopy. The dispersive conduction bands and the spin–orbit split Yb 4f7/2 and 4f5/2 states were observed clearly near the Fermi level. We revealed that a flat band located −80meV below the 4f7/2 state shows a momentum-dependent behavior around the M¯ point of the surface Brillouin zone, and it was described by a hybridization-band picture based on the periodic Anderson model. We attributed the observed momentum-dependent behavior to the effect of hybridization between the conduction and 4f electrons in the subsurface region of YbInCu4.

Variational Wavefunction for the Periodic Anderson Model with Onsite Correlation Factors

We propose a variational wavefunction containing parameters to tune the probabilities of all the possible onsite configurations for the periodic Anderson model. We call it the full onsite-correlation wavefunction (FOWF). This is a simple extension of the Gutzwiller wavefunction (GWF), in which one parameter is included to tune the double occupancy of the f electrons at the same site. We compare the energy of the GWF and the FOWF evaluated by the variational Monte Carlo method and that obtained with the density-matrix renormalization group method. We find that the energy is considerably improved in the FOWF. On the other hand, the physical quantities do not change significantly between these two wavefunctions as long as they describe the same phase, such as the paramagnetic phase. From these results, we not only demonstrate the improvement by the FOWF, but we also gain insights on the applicability and limitation of the GWF to the periodic Anderson model.

Effect of c-f hybridization on electric and magnetic properties of some Heavy Fermion (HF) systems

Representing the heavy fermion systems by the Periodic Anderson Model (PAM), we have used Zubarev technique to see the effect of c-f hybridization on the temperature dependence of resistivity and magnetic susceptibility. The calculated resistivity and magnetic susceptibility show the general features observed in these materials experimentally. Further, we have shown how the strength of hybridization as well as the position of the f-level affects both the properties and the Kondo temperature of these systems.

Mott transitions in the periodic Anderson model

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.

Transport properties of bilayer graphene nanoribbons with hydrogen adatoms

The transport characteristics of bilayer graphene nanoribbons with hydrogen adatoms in an external static electric field is studied. The adsorption of hydrogen atoms on the surface of bilayer graphene ribbons is considered within the single-impurity periodic Anderson model. The transport coefficients of impurity-doped bilayer graphene ribbons are simulated in the relaxation time approximation. At a constant concentration of hydrogen adatoms, a nonlinear dependence of the transport coefficients on the static electric field strength has been revealed. It is found that the electrical conductivity and the diffusion coefficient of electrons in bilayer graphene ribbons decrease with increasing concentration of hydrogen adatoms.

Impurity-induced antiferromagnetic domains in the periodic Anderson model

A central feature of the Periodic Anderson Model is the competition between antiferromagnetism, mediated by the Ruderman-Kittel-Kasuya-Yosida interaction at small conduction electron-local electron hybridization $V$, and singlet formation at large $V$. At zero temperature, and in dimension $d>1$, these two phases are separated by a quantum critical point $V_c$. We use Quantum Monte Carlo simulations to explore the effect of impurities which have a local hybridization $V_{*} < V_c$ in the AF regime which are embedded in a bulk singlet phase with $V > V_c$. We measure the suppression of singlet correlations and the antiferromagnetic correlations which form around the impurity, as well as the size of the resulting domain. Our calculations agree qualitatively with NMR measurements in CeCoIn$_{5-x}$Cd$_x$.