Session V07: Kondo and Anderson Lattice Physics

Tricritical Points in the Underscreened Anderson Lattice Model

We report calculations on the Underscreened Anderson Lattice Model that has been proposed to describe the Hidden Ordered phase of URu2Si2. Since the proposed Hidden Ordered Phase is associated with a spin-orbital density wave, in which the spins condense in a spontaneously chosen plane, the magnetic properties become anisotropic in the low temperature phase. The ansiostropy is similar to that found by magnetic torque measurements. We examine the field-temperature phase diagram. At zero field, the transition to the Hidden Ordered phase is second order. The application of a magnetic field has the effect of reducing the transition temperature towards zero. However, at a critical value of the applied field, the transition becomes first-order in agreement with high field measurements. We present an analysis of the tricritical point, which shows that the upper critical dimension of the model is reduced to d=3. Therefore, the transition may be reasonably described by a Gaussian approximation.   

Schwinger boson approach to the Kondo lattice model

The microscopic mechanism of the heavy-fermion systems close to anti-ferromagnetic quantum critical point constitutes an outstanding open problem in correlated electron systems. To address this issue, we employ a distinct route from the dynamical mean-field theory by solving the 2D Kondo-Heisenberg model via a dynamical large-N multichannel Schwinger boson approach. We identify the quantum critical point separating the anti-ferromagnetic long-ranged ordered and the heavy Kondo-screened Fermi-liquid phases. Various thermodynamical observables near criticality show non-Fermi liquid behaviors and agree qualitatively well with the experiments seen in CeCu_6-xAu_x and YbRh₂Si₂.   

The splitting of electrons on the Kondo lattice

We demonstrate that strong correlations in Kondo lattice models can be organised around a splitting of the electronic degree of freedom. This provides a fresh perspective on the behaviour of local moment systems, in which the formation of a heavy fermion band and violation of the Luttinger sum rule are naturally accounted for.   

The 4f electron character on core-level spectroscopies of AuCu3-type Ce intermetallics

The 3d transition metal compounds and 4f rare earth compounds show attractive phenomena, such as superconductivity and Kondo effect, due to strong electron correlations among localized 3d and 4f electrons. Especially, the 4f electron state of Ce intermetallics causes the various phenomena of Ce intermetallics, Kondo effects and magnetic ordering, for example.
X-ray core-level spectroscopy is an efficient technique to investigate the electronic states of strongly correlated systems. Recent years, experimental techniques have been rapidly developing and, especially, the progress in experimental resolution has enabled us to observe fine spectral features, which were not formerly observed. These advantages will enable us to observe spectral fine features related with the 4f electron state related to Kondo effects and/or magnetic ordering of the Ce intermetallics.
In this study, we discuss 4f electron character of AuCu3-type Ce intermetallics by means of X-ray spectra, especially paying attention on the polarization dependence and the incident photon energy. In order to simulate the electronic state of AuCu3-type Ce intermetallics, we use an impurity Anderson model including realistic valence structure.   

Synchrotron-Mossbauer study of the pressure-driven magnetic evolution in EuGa4

Rare-earth Eu compounds represent an intriguing class of magnetic materials that provide a competing playground of Kondo physics, RKKY exchange interactions, and valence evolution. Here, we explore the evolution of antiferromagnetism under pressure via synchrotron-based Mossbauer spectroscopy. Contrary to previous electrical transport results, our observation provides direct evidence of a magnetic ground state at high pressure, continuous through a first order phase transition at 5 GPa and persisting to at least 13.6 GPa. We discuss this result in the framework of a potential interaction between evolution of the valence condition and an increase in the ordering temperature.
  

Order fractionalization and the two channel Kondo lattice

The symmetric two-
channel Kondo lattice, involving two separate conduction electron seas, inter-
acting with a lattice of local moments, provides an idealized model for the
novel cubic heavy electron superconductors, PrX₂Al₂₀, (X=Ti, Va) and UBe₁₃.
There are many indications that two-channel Kondo lattice is unstable to the
development of broken channel symmetry, in which the Kondo effect develops
selectively in one channel giving rise to a \channel magnetization" We study
this novel phase using the large N expansion. One of the remarkable features
of the resulting mean-field theory, is the emergence of a two-component spinor
describing the channel magnetization, suggesting the possibility of order frac-
tionalization. Using the large N expansion, we show that the long-wavelength
physics of the two-channel Kondo lattice is described by the principle chiral
model, in which the skyrmion density of the channel magnetization couples to
the difference of the electromagnetic and internal gauge fields. We will discuss
the implications of these results for the order fractionalization conjecture and
possible observable consequences.   

Impact of Rashba spin-orbit coupling on f-electron materials

We study the interplay between Rashba spin-orbit coupling (RSOC) and the Kondo screening in noncentrosymmetric f-electron materials. We show that the Kondo interaction of the f-electrons becomes anisotropic at high temperatures due to the RSOC in these materials leading to a suppression of the Kondo temperature. However, an isotropic Kondo effect is restored at low temperature which leads to a complete Kondo screening. We furthermore demonstrate that the Kondo effect has influence on the Rashba splitting in the band structure, which becomes temperature dependent. We show that although f electrons are localized at temperatures above the Kondo temperature, already at these temperatures a helical spin polarization emerges. With decreasing temperature, the Kondo screening occurs, which leads to drastic changes in the band structure. Remarkably, these changes in the band structure depend on the helical spin polarization. For strong RSOC, we observe that one of the helical bands becomes gapped at low temperature and a helical half-metal is formed.
  

Charge and heat transport in a charge 2 channel Kondo device

Recently, the charge two channel effect was realized in an experimental setup for the first time. Remarkably, the scaling curve of the critical conductance was measured over many decades and was in excellent agreement with theoretical calculations. In this talk we focus on the heat transport in the setup. We theoretically show a violation of the Wiedemann-Franz law and point out an interesting connecting to the central charge of one dimensional Majorana fermions.   

Coupled charge-Kondo quantum dot devices

Exquisite experimental control over exotic states of quantum matter has recently been demonstrated in charge-Kondo quantum dot devices [1,2]. These systems constitute a new paradigm for circuit realizations of fundamental models of quantum criticality, with essentially perfect agreement between experiment and theory for fractionalized two-channel and three-channel Kondo physics [2,3].

Here we study theoretically a device comprising two charge-Kondo quantum dots, coupled together by a quantum point contact. This system is the first step towards constructing more elaborate nanodevices using charge-Kondo building blocks, which could eventually lead to quantum simulations of exotic lattice models.

Depending on dot occupation, different variants on the classic two-impurity Kondo model can be realized, and clear signatures of quantum criticality show up in measurable conductance as a function of tunable parameters.

[1] Iftikhar et al, Nature 526, 233 (2015)
[2] Iftikhar et al, Science 360, 1315 (2018)
[3] Mitchell et al, PRL 157202 (2016)   

Higher-order Fermi-liquid corrections for thermo-electric transport through an Anderson impurity

There has been an important progress recently in the Fermi-liquid theory for Kondo systems away from half-filling [1,2]. That clarifies what are the essential parameters that determine the non-equilibrium impurity Green's function G(ω,T,eV) at low frequencies ω, temperatures T, and bias voltages eV, in the particle-hole asymmetric case. The asymptotically exact Green's function away from half-filling are shown to be determined, up to order ω², T², and (eV)², by the static linear susceptibilities of the impurity occupation numbers and the corresponding non-linear susceptibilities that are defined with respect to the equilibrium ground state. In the present work, we apply a microscopic description that uses the Ward identities [2] to thermo-electric transport of quantum dots and dilute magnetic alloys. Using also the NRG approach, we explore how the three-body correlations that enter through the non-linear susceptibilities contribute to thermal conductivity at zero and finite magnetic fields.
[1] M. Filippone, C. Moca, A. Weichselbaum, J. von Delft, and C. Mora, PRB 98, 075404 (2018); C. Mora, C. Moca, J. von Delft, and G.Zaránd, PRB 92, 075120 (2015).
[2] A. Oguri and A. C. Hewson, PRL 120, 126802 (2018); PRB 97, 043508 (2018); PRB 97, 035435 (2018); PRB 98, 079905(E)(2018).   

Tracking incommensurate magnetism with Slave Boson Mean Field Theory

Accounting for strong correlations is one of the most challenging problems in solid state physics,
and has given rise to the development of a plethora of different methodological approaches. Among them, the slave boson mean field formalism has been shown to successfully describe strongly correlated electron systems such as heavy fermion physics and quantum impurity models. While DMFT is another popular method of use within the scope of these systems, the slave boson mean field method can be applied to problems beyond the reach of DMFT, and such provide an interesting complementary view. In particular, this applies
to models with large Hilbert spaces, and especially the investigation of incommensurate magnetic order where the magnetic unit cell would be too large to describe it within any cluster DMFT framework. Therefore, slave boson mean field is well suited to fill a niche in contemporary methods of condensed matter physics. This talk intends to elaborate on the method of spin rotation invariant slave boson mean
field theory including fluctuations around the saddle point, and its applications to the periodic Anderson model.   

Correlation effects in the emergence of Bound Spin State in the Continuum

Bound States in the Continuum (BICs) are states with localized wave-function even though lying in the continuum. Here, we explore theoretically the emergence of a Spin-BIC in a system comprising two identical quantum dots side-coupled to a quantum wire. The dots are symmetrically coupled to the site at the center of the wire and to its nearest neighbors. Taking advantage of the dot symmetry, we work with the bonding and anti-bonding (AB) levels resulting from the symmetric and antisymmetric combinations of the dot levels. We consider a Two-Impurity Anderson model. In the non-interacting limit (U=0), the AB orbital is decoupled from the conduction band and is hence a BIC. For U≠0, our Numerical Renormalization-Group results show that the interaction couples the bonding and anti-bonding orbitals and hence broadens the latter. The RKKY interaction between the magnetic moments of the two dots can either be ferro- or antiferromagnetic, to form a singlet or a triplet, which affects the formation of the Kondo cloud. In the strongly particle-hole asymmetric coupling limit, the AB orbital is reduced to a singly occupied level that is decoupled from the continuum, i.e., a Spin-BIC.   

Maximally Localized Wannier Orbitals and the Anderson Impurity Model for Twisted Bilayer Graphene

We developed an effective Anderson impurity model to describe the low energy electronic properties of the twisted bilayer graphene. By using the method of selectively localizing Wannier orbitals, we construct a model that captures the key energetic and symmetry features of the original low energy bands and is possible for further calculation with non-perturbative methods. Using this model, we investigated the effect of interaction and the applied magnetic field near the half-filled region.   

Impact of Quenched Disorders on The Holstein Model

Over the last few decades, there has been considerable interest in the effects of disorder on the competition between superconductivity and
charge order wave (CDW) in underdoped cuprates. Similar questions arise in the study of the interplay of polaron formation and ordering with Anderson localization in disordered electron-phonon systems such as superconducting peroskites, and colossal magnetoresistance manganites. Many interesting phenomena are observed including non-Fermi liquid behavior and metal-insulator transitions (MIT) due to the opening of a CDW gap or due to Anderson localization. The combination of electron-phonon coupling and randomness leads to rich phase regimes as the phonon frequency ω, electron-phonon coupling λ and disorder strength △ vary. Here we present results from the DQMC method for the two-dimensional disordered Holstein model. We focus on the dependence of sizes of domain walls as well as the correlation length of density fluctuations. We also show the results for the temperature dependence of the conductance and compare to existing dynamical mean field theory results.   

Universal entanglement of typical states in constrained systems

We develop a formalism to exactly evaluate the bipartite entanglement of random states in large Hilbert spaces with local and global constraints. We solve the simplest class of constraints which includes the much studied Rydberg-blockaded/Fibonacci chain. The resulting entanglement spectra may be classified into `phases’ depending on their singularities. Our results predict the entanglement of infinite temperature eigenstates in thermalizing constrained systems and provide a baseline for numerical studies.