Session X44: Kondo and Anderson Lattice Physics

The Order Fractionalization Hypothesis: Applications to Heavy Electron and Strongly Correlated Materials

Landau's theory of phase transitions places no à priori constraint on the microscopic nature of broken symmetry, but in electronic systems we generally assume that an order parameter involves an even number of electrons or holes: the basis of the Hartree-Fock, BCS paradigm. The Order Fractionalization Hypothesis proposes an alternative class of half-integer spin or odd-integer charge condensate, resulting from the spontaneous formation of symmetry-breaking bound, composite fermions. Here, the bound-state wavefunction, which carries half-integer spin or odd-integer charge acts as a bosonic condensate. Using mean-field and numerical RG techniques, we demonstrate this idea using the two-channel Kondo problem, showing that various different classes of three-body bound-state formation develop in response to different applied patterns of channel symmetry breaking. In a lattice, these various patterns of symmetry breaking feed back to drive spontaneous three-body bound-state formation, inducing a form of order that lies outside the Hartree-Fock BCS paradigm. We discuss a provisional categorization of fractionalized order and possible applications to heavy fermion and other strongly correlated materials.   

Low-carrier Density and Fragile Magnetism in a Kondo Lattice System

Known low-carrier Kondo systems evolve from metallic non-magnetic analogues, while a recent theoretical model for the dilute carrier Kondo limit predicts semimetallic behavior. Very few 4f low-carrier Kondo systems have been reported, mostly based on Ce. In this talk, I will show evidence for low-carrier Kondo behavior in Yb₃Ir₄Ge₁₃ with a low carrier background as illustrated by the non-magnetic analogue Lu₃Ir₄Ge₁₃. A fragile magnetic state occurs in the Yb compound at very low temperatures, which, together with the semimetalic behavior, can be understood within the framework of the dilute-carrier limit of a Kondo lattice model. An entirely new regime of the Kondo effect is discovered, where the fragile magnetism can also be tuned in a non-Fermi liquid fashion through Lu-for-Yb substitution.   

Reduction of the ordered-magnetic moment and its relationship to Kondo coherence in Ce1-xLaxCu2Ge2

The microscopic details of the suppression of antiferromagnetic order in the Kondo-lattice series Ce_1-xLa_xCu₂Ge₂ due to nonmagnetic dilution by La are revealed through neutron diffraction results for x=0.20, 0.40, 0.75, and 0.85. Magnetic Bragg peaks are found for 0.20≤x≤0.75, and both the Neel temperature, T_N, and the ordered magnetic moment per Ce, µ, linearly decrease with increasing x. The reduction in µ points to strong hybridization of the increasingly diluted Ce 4f electrons, and we find a remarkable quadratic dependence of µ on the Kondo-coherence temperature. We discuss our results in terms of local-moment- versus itinerant-type magnetism and mean-field theory, and show that Ce_1-xLa_xCu₂Ge₂ provides an exceptional opportunity to quantitatively study competing magnetic interactions in a Kondo lattice.
arXiv:1710.08329   

Log-rise of the Resistivity in a Holographic Kondo Model

We study a single channel Kondo effect using a recently developed holographic large-N technique. In order to obtain resistivity of this model, we introduce a probe field. The gravity dual of a localized fermionic impurity in 1+1 dimensional host matter is constructed by embedding a localized AdS₂-brane in the bulk of AdS₃. This helps us construct an impurity charge density which acts as a source to the bulk equation of motion of the probe gauge field. Our choice of parameters tunes the near boundary impurity current to be marginal, resulting in a log-T behavior in the UV resistivity, as is expected for the Kondo problem. The resistivity at the IR fixed point turns out to be zero, signaling a complete screening of the impurity.   

Thermal transport in a charge two-channel Kondo setup

The original Kondo model describes the behaviour of a non-magnetic metal containing a single magnetic impurity. Motivated by the experimental realization of a remarkable quantum dot device [Iftikhar et al., Nature 526, 233 (2015)], we consider the more complicated charge two-channel Kondo (2CK) model. In particular, we discuss the thermal transport properties of this 2CK model due to a temperature gradient between the leads. We propose that the corresponding heat conductance provides a way to experimentally verify the Majorana character of the dot region at the critical non-Fermi liquid point.   

Nambu-Goldstone fermions in supersymmetric lattice fermion models

The relation between spontaneous symmetry breaking and gapless excitations
called Nambu-Goldstone (NG) bosons has been well understood in
both relativistic and non-relativistic systems. On the other hand,
less is known about the relation between spontaneous supersymmetry (SUSY)
breaking and NG modes in non-relativistic systems. To close this gap, we
introduce and study two lattice fermion models with SUSY in (1+1) dimension
[1,2], which are generalizations of the Nicolai model [3].
In each model, the Hamiltonian is built from two supercharges. The
supercharges have one adjustable parameter, and are comprised solely of
fermion operators. Under certain conditions, we prove that SUSY is
spontaneously broken in both finite and the infinite systems. Then, by
combining analytical and numerical methods, we show that there exist
gapless modes that can be thought of as NG fermions associated with
spontaneous SUSY breaking. We also discuss the dispersion relation of the
NG fermions in each model.

[1] N. Sannomiya, H. Katsura and Y. Nakayama, Phys. Rev. D 94, 045014 (2016).
[2] N. Sannomiya, H. Katsura and Y. Nakayama, Phys. Rev. D 95, 065001 (2017).
[3] H. Nicolai, J. Phys. A 9, 1497 (1976).   

Fermi Arcs in Anderson Lattice Models with d-wave Hybridization

We study an Anderson lattice model with a d-wave hybridization gap, using a second-order perturbation theory. Due to the interaction, the heavy electrons acquire a finite lifetime, while the light electrons do not. This asymmetric electron lifetime, combined with the momentum-dependent hybridization gap, results in Fermi arcs in electron’s spectrum function.   

Exact Boson-Fermion Duality on a 3D Euclidean Lattice

Recently there has been much interest in an IR "Boson-Fermion duality" in 3 spacetime dimensions. This duality generates many more dualities, forming the so-called "duality web"; some of these dualities have been extremely helpful in understanding intricate problems such as half-filled Landau level, insulator-superconductor transition, surface of strongly interacting topological insulator, etc. Despite the usefulness of these dualities, a solid foundation of them was in need. In this talk I will present how the elementary Boson-Fermion duality can be UV-completed as an exact mapping of lattice gauge theories, thereby providing a simple, non-perturbative proof of the IR Boson-Fermion duality and hence the entire duality web.   

Doped Kondo chain - a heavy Luttinger liquid

The doped one dimensional Kondo Lattice describes complex competition between itinerant and magnetic ordering. The numerically computed wave-vector dependent charge and spin susceptibilities give new insights to its low energy properties. Similarly to the prediction of the Large-N approximation, gapless spin and charge modes appear at the large Fermi wave-vector. The highly suppressed spin velocity is a manifestation of ``Heavy'' Luttinger liquid quasiparticles. A low energy hybridization gap is detected at the small (conduction band) Fermi wave-vector. In contrast to the exponential suppression of the Fermi velocity in the Large-N approximation, we fit the spin velocity by a density dependent power law of the Kondo coupling. The differences between the Large-N theory and our numerical results are associated with the emergent magnetic RKKY interactions.   

Higher-order Fermi-liquid corrections for an Anderson impurity away from half-filling

We extend the microscopic Fermi-liquid theory for the Anderson impurity to explore non-equilibrium transport at finite magnetic fields. Using the Ward identities with the analytic and anti-symmetric properties of the vertex function, the Fermi-liquid corrections of order T² and (eV)² are determined at low temperatures T and low bias voltages eV [1]. The results can be compared with those obtained recently in the Nozières phenomenological description [2]. Away from half-filling, these corrections can be expressed in terms of the linear and non-linear static susceptibilities which represent the two-body flucutuations (2BF) and three-body fluctuations (3BF), respectively. We calculate these coefficients for the conductance through a quantum dot using the numerical renormalization group. At zero magnetic field, the 2BF dominate the corrections in the Kondo regime. The 3BF become significant far away from half-filling, especially in the valence-fluctuation regime and empty-orbital regimes. In contrast, at finite magnetic fields, the contributions of the 3BF become comparable to those of the 2BF.

[1] A. Oguri and A. C. Hewson, arXiv:1709.06385; arXiv:1710.02948; arXiv:1710.04575.
[2] M. Filippone, C. Moca, J. von Delft, and C. Mora, Phys. Rev. B 95, 165404 (2017).   

Skyrmion defects and competing singlet orders in an antiferromagnetic Kondo lattice

The global phase diagram of antiferromagnetic heavy fermions [1] raises the issue of how to access the paramagnetic, spin singlet states from the antiferromagnetic order. We study a honeycomb Kondo lattice starting from a non-linear sigma model representation of the local moments. The skyrmion defects of the latter are known to induce singlet orders from a perturbative gradient expansion [2]. Based on an effective Dirac Hamiltonian in the skyrmion background, we search for the various singlet orders which signify the spin singlet states upon the condensation of the skyrmions in the antiferromangetically disordered regime. We find two leading singlet channels, one in the spin Peierls and the other in the Kondo singlet [3]. The relative stability of the two are studied by varying the Kondo coupling [3]. Our results provide new insight into the global phase diagram of the heavy fermion systems.

[1] Q. Si, Phys. Status Solidi 247, 476 (2010); Physica B 378, 23 (2006).
[2] P. Goswami and Q. Si, Phys. Rev. B 89, 045124 (2014).
[3] C.C.Liu, P. Goswami and Q. Si, Phys. Rev. B 96, 125101 (2017)

  

Quantum Quench of the One-Dimensional Kondo Lattice Model

The remarkable progress in the time-resolved experimental techniques has made it possible to probe ultrafast dynamics in strongly correlated electron materials and quantum quenches in interacting cold atoms. Motivated by recent pump-probe experiments on the ultrafast dynamics of colossal magnetoresistive (CMR) materials~[1,2], here we study the quench dynamics of one-dimensional (1D) ferromagnetic Kondo-lattice model which serves as a useful toy model for CMR transition metal oxides such as mangnites~[3]. The 1D Kondo-lattice model exhibits a rich phase diagram including a ferromagnetic phase, a phase separation regime, and a paramagnetic phase~[3]. Similar phases are believed to also appear in higher dimensional models. Using time-dependent density-matrix renormalization group method, we investigate the nonequilibrium dynamics of spin correlations in quenches from the ferromagnetic to the disordered phases and vice versa. We also present the real-time development of inhomogeneity as the system is quenched into the phase separation regime.

[1] R. D. Averitt, et al. Phys. Rev. Lett. 87, 017401 (2001).
[2] Y. H. Ren, et al. Phys. Rev. B 78, 014408 (2008).
[3] S. Yunoki, et al. Phys. Rev. Lett. 80, 845 (1998).   

Time-Dependence of the Kondo Screening Cloud Following a Quench

We use the time-dependent numerical renormalization group to study time evolution following quenches in variants of the Kondo model. Quantities of interest include the expectation value of the impurity spin in broken-symmetry states, the overlap between the wave functions before and after the quench, and the quantum entanglement between the region around the impurity and the rest of the system. For the conventional Kondo model of a spin-half impurity in a metallic host, we focus on the effects of sudden switching on or off of the impurity-host exchange coupling. In the pseudogap Kondo model, we investigate quenches that take the system through a quantum critical point between a Kondo phase and a local-moment phase in which the impurity moment is asymptotically decoupled from the band at low temperatures.   

Double Singlet Pair in the Kondo Ground-State

In the Kondo ground-state the magnetic impurity d₀ forms a singlet state with the conduction electrons, i.e., with one localized electron state a₀ composed of the conduction band. This state a₀ has the opposite spin as d₀ and has maximum amplitude at the impurity. In the sub-band with the same spin as d₀ the electrons try to minimize the amplitude at the impurity. This is achieved by avoiding a second localized state b₀ with maximum amplitude at d₀, i.e. leaving b₀ empty. Although one might expect that the singlet state (d₀,a₀) between d₀ and a₀ represents the full Kondo ground-state, this is not the case. The system forms a combination of two singlet pairs: (d₀,a₀) and (d₀,b₀). This is counter intuitive because (d₀,b₀) has a relative large Ising energy. But its spin-flip matrix element is not reduced by orthogonality. The dominant energy reduction in the ground-state is due to the mixed terms between the individual pairs. Despite the long history of the Kondo effect the importance of this composition of the Kondo ground-state has been overlooked so far.
  

Anomaly in temperature-dependent electronic structures of heavy fermion compound CeB6

The temperature-dependent electronic structures of heavy fermion compound CeB₆ were investigated thoroughly by means of the combination of density functional theory and single-site dynamical mean-field theory. The band structure, density of states, and 4f valence state fluctuation of CeB₆ were calculated in a broad temperature range of 10 ∼ 120 K. Overall, the 4f electrons remain incoherent, approximately irrespective of environment temperature. However, we find that these observables exhibit some unusual features near 20 K. In addition, the evolutions of 4f orbital occupancy, total angular momentum, and total energy with respect to temperature show apparent non-monotonic behaviors around 20 K. The possible explanations for these tantalizing characteristics are discussed concisely.