The observation of a separation between the antiferromagnetic phase boundary and the small-large Fermi surface transition in recent experiments has led to the proposal that frustration is an important additional tuning parameter in the Kondo lattice model of heavy fermion materials. The introduction of a Kondo (K) and a frustration (Q) axis into the phase diagram permits us to discuss the physics of heavy fermion materials in a broader perspective. The current experimental situation is analysed in the context of this combined "QK" phase diagram. We discuss various theoretical models for the frustrated Kondo lattice, using general arguments to characterize the nature of the $f$-electron localization transition that occurs between the spin liquid and heavy Fermi liquid ground-states. We concentrate in particular on the Shastry--Sutherland Kondo lattice model, for which we establish the qualitative phase diagram using strong coupling arguments and the large-$N$ expansion. The paper closes with some brief remarks on promising future theoretical directions.
Magnetic frustration, which is well-defined in insulating systems with localized magnetic moments, yields exotic ground states like spin ices, spin glasses, or spin liquids. In metals magnetic frustration is less well defined because of the incipient delocalization of magnetic moments by the interaction with conduction electrons, viz., the Kondo effect. Hence, the Kondo effect and magnetic frustration are antithetic phenomena. Here we present experimental data of electrical resistivity, magnetization, specific heat and neutron diffraction on CePdAl, which is one of the rare examples of a geome…
We calculated the phase diagram of the Kondo-Heisenberg model on two-dimensional honeycomb lattice with both nearest-neighbor and next-nearest-neighbor antiferromagnetic spin exchanges, to investigate the interplay between RKKY and Kondo interactions at presence of magnetic frustration. Within a mean-field decoupling technology in slave-fermion representation, we derived the zero-temperature phase diagram as a function of Kondo coupling $J_k$ and frustration strength $Q$. The geometrical frustration can destroy the magnetic order, driving the original antiferromagnetic (AF) phase to non-magnet…
We analyze a microscopic origin of the Kondo effect-assisted orbital order in heavy-fermion materials. By studying the periodic two-orbital Anderson model with two local electrons, we show that frustration of Hund's rule coupling due to the Kondo effect leads to an incommensurate spiral orbital and magnetic order, which exists only inside the Kondo screened (heavy-electron) phase. This spiral state can be observed in neutron and resonant X-ray scattering measurements in ${\rm U}$- and ${\rm Pr}$-based heavy-fermion compounds, and realized in cold atomic gases, e.g. fermionic ${}^{173}{\rm Yb}$…
We study the competition between the Kondo effect and frustrating exchange interactions in a Kondo-lattice model within a large-${\cal N}$ dynamical mean-field theory. We find a T=0 phase transition between a heavy Fermi-liquid and a spin-liquid for a critical value of the exchange $J_c = T_{K}^0$, the single-impurity Kondo temperature. Close to the critical point, the Fermi liquid coherence scale $T^\star$ is strongly reduced and the effective mass strongly enhanced. The regime $T>T^\star$ is characterized by spin-liquid magnetic correlations and non-Fermi-liquid properties. It is suggested t…
We report results of isothermal magnetotransport and susceptibility measurements at elevated magnetic fields B down to very low temperatures T on high-quality single crystals of the frustrated Kondo-lattice system CePdAl. They reveal a B*(T) line within the paramagnetic part of the phase diagram. This line denotes a thermally broadened 'small'-to-'large' Fermi surface crossover which substantially narrows upon cooling. At B_0* = B*(T=0) = (4.6 +/- 0.1) T, this B*(T) line merges with two other crossover lines, viz. Tp(B) below and T_FL(B) above B_0*. Tp characterizes a frustration-dominated spi…
Hexagonal CeRhSn with paramagnetic $4f$ moments on a distorted Kagome lattice displays zero-field quantum critical behavior related to geometrical frustration. We report high-resolution thermal expansion and magnetostriction measurements under multiextreme conditions such as uniaxial stress up to 200 MPa, temperatures down to 0.1 K and magnetic fields up to 10 T. Under uniaxial stress along the $a$-direction, quantum criticality disappears and a complex magnetic phase diagram arises with a sequence of phases below 1.2 K and fields between 0 and 3 T ($\parallel a$). Since the Kondo coupling inc…
We investigate the ground state of the Kondo necklace model on geometrically-frustrated lattices by the variational Monte Carlo simulation. To explore the possibility of a partially-ordered phase, we employ an extension of the Yosida-type wave function as a variational state, which can describe a coexistence of spin-singlet formation due to the Kondo coupling and magnetic ordering by the Ruderman-Kittel-Kasuya-Yosida interaction. We show the benchmark of the numerical simulation to demonstrate the high precision brought by the optimization of a large number of variational parameters. We discus…
Competition between Geometrical Frustration and the Kondo Effect in CePdAl Revealed by High-Resolution Magnetization
Institute for Solid State Physics, The University of Tokyo（东京大学固体物理研究所）；Nagoya Institute of Technology（名古屋工业大学）；Institute for Materials Research, Tohoku University（东北大学物质材料研究所）；School of Science and Engineering, Chuo University（中央理工学院）；Department of Basic Science, The University of Tokyo（东京大学基础科学系）；Graduate School of Science and Engineering, Univ. of Toyama（富山理工学研究院）
We investigate the effect of geometrical frustration on the competition between the Kondo coupling and the Ruderman-Kittel-Kasuya-Yosida interaction in Kondo lattice systems. By variational Monte Carlo simulations, we reveal an emergent quantum phase with partial ordering in which the frustration is relieved by forming a magnetic order on a sublattice and leaving the rest in the Kondo screening with spin-singlet formation. The role of quantum fluctuations and spin-charge interplay is elucidated.
The quantum phase transition from a spin-Peierls phase with a small Fermi surface to a paramagnetic Luttinger-liquid phase with a large Fermi surface is studied in the framework of a one-dimensional Kondo-Heisenberg model that consists of an electron gas away from half filling, coupled to a spin-1/2 chain by Kondo interactions. The Kondo spins are further coupled to each other with isotropic nearest-neighbor and next-nearest-neighbor antiferromagnetic Heisenberg interactions which are tuned to the Majumdar-Ghosh point. Focusing on three-eighths filling and using the density-matrix renormalizat…
We investigate single crystalline samples of Ce$_{1-x}$Nd$_{x}$RhIn$_{5}$ by means of X-ray diffraction, microprobe, magnetic susceptibility, heat capacity, and electrical resistivity measurements. Our data reveal that the antiferromagnetic transition temperature of CeRhIn$_{5}$, $T_{N}^{\mathrm{Ce}} = 3.8$ K, is linearly suppressed with $x_{\mathrm{Nd}}$, by virtue of the "Kondo hole" created by Nd substitution. The extrapolation of $T^{\mathrm{Ce}}_{N}$ to zero temperature, however, occurs at $x_{c} \sim 0.3$, which is below the 2D percolation limit found in Ce$_{1-x}$La$_{x}$RhIn$_{5}$. Thi…
These lecture notes give a brief introduction to heavy fermion physics, emphasizing aspects of particular modern interest. Following an introduction to the Kondo effect and the phenomenology of heavy fermions, the article introduces Kondo insulators, the simplest heavy fermions; the large N expansion for the Kondo lattice; heavy fermion superconductivity including the symplectic N approach; topological Kondo insulators and finally a discussion of the challenge of understanding the co-existence of magnetism and the Kondo effect.
We consider a ring of three quantum dots mutually coupled by antiferromagnetic exchange interactions, and tunnel-coupled to two metallic leads: the simplest device in which the consequences of local frustration arising from internal degrees of freedom may be studied within a 2-channel environment. Two-channel Kondo (2CK) physics is found to predominate at low-energies in the mirror-symmetric systems considered, with a residual spin 1/2 overscreened by coupling to both leads. It is however shown that two distinct 2CK phases, with different ground state parities, arise on tuning the interdot exc…
Magnetic fluctuations induced by geometric frustration of local Ir-spins disturb the formation of long range magnetic order in the family of pyrochlore iridates, R$_{2}$Ir$_{2}$O$_{7}$ (R = lanthanide)$^{1}$. As a consequence, Pr$_{2}$Ir$_{2}$O$_{7}$ lies at a tuning-free antiferromagnetic-to-paramagnetic quantum critical point and exhibits a diverse array of complex phenomena including Kondo effect, biquadratic band structure, metallic spin-liquid (MSL), and anomalous Hall effect$^{2-5}$. Using spectroscopic imaging with the scanning tunneling microscope, complemented with machine learning K-…
We discuss a physical mechanism of a non-BCS nature which can stabilize a superconducting state in a {\it strongly repulsive} electronic system. By considering the two-dimensional Hubbard model with spatially modulated electron hoppings, we demonstrate how kinetic-energy frustration can lead to robust d-wave superconductivity at {\it arbitrarily} large on-site repulsion. This phenomenon should be observable in experiments using fermionic atoms, e.g. ${}^{40}K$, in specially prepared optical lattices.
We study the interplay between the spin-liquid and Kondo physics, as related to the non-magnetic part of the phase diagram of heavy fermion materials. Within the unrestricted mean-field treatment of the infinite-$U$ 2D Anderson-Heisenberg model, we find that there are two topologically distinct non-degenerate uniform heavy Fermi liquid states that may form as a consequence of the Kondo coupling between spinons and conduction electrons. For certain carrier concentrations the uniform Fermi liquid becomes unstable with respect to formation of a new kind of anharmonic "Kondo stripe" state with inh…
Geometric frustration adds a new competing energy scale to the antiferromagnetic (AFM) Kondo lattice model (KLM). In this work, we systematically study the doniach phase diagram on the square and triangular lattices in the same theoretical framework and reveal unexpected responses of it on the two lattices. The potential energy created by the geometric frustration is comparable to the Ruderman-Kittel-Kasuya-Yosida (RKKY) coupling, which completely suppresses the long-range antiferromagnetic (AFM) order on the half-filled triangular lattice. While, on the square lattice, the long-range AFM orde…
Inspired by the recent experimental evidence of antiferromagnetism and superconductivity coexistence in heavy fermion CeRhIn$_5$, we propose a fully microscopic approach based on the idea of real space pairing within the Anderson-Kondo lattice model. We present an overall phase diagram incorporating the emergence of a quantum critical point, where Kondo insulating (KI), antiferromagnetic (AF) and superconducting (SC) phases meet. We also obtain the Kondo insulating state with totally compensated magnetic moments as the parental state for the emerging SC phases. Furthermore, the coexistent (AF+…
In the heavy-fermion metal CePdAl long-range antiferromagnetic order coexists with geometric frustration of one third of the Ce moments. At low temperatures the Kondo effect tends to screen the frustrated moments. We use magnetic fields $B$ to suppress the Kondo screening and study the magnetic phase diagram and the evolution of the entropy with $B$ employing thermodynamic probes. We estimate the frustration by introducing a definition of the frustration parameter based on the enhanced entropy, a fundamental feature of frustrated systems. In the field range where the Kondo screening is suppres…
The absence of negative sign problem in quantum Monte Carlo simulations of spin and fermion systems has different origins. World-line based algorithms for spins require positivity of matrix elements whereas auxiliary field approaches for fermions depend on symmetries such as particle-hole. For negative-sign-free spin and fermionic systems, we show that one can formulate a negative-sign-free auxiliary field quantum Monte Carlo algorithm that allows Kondo coupling of fermions with the spins. Using this general approach, we study a half-filled Kondo lattice model on the Honeycomb lattice with geo…
The interplay between Kondo effect, indirect magnetic interaction and geometrical frustration is studied in the Kondo lattice on the one-dimensional zigzag ladder. Using the density-matrix renormalization group (DMRG), the ground state and various short- and long-range spin- and density-correlation functions are calculated for the model at half-filling as a function of the antiferromagnetic Kondo interaction down to $J=0.3t$ where $t$ is the nearest-neighbor hopping on the zigzag ladder. Geometrical frustration is shown to lead to at least two critical points: Starting from the strong-$J$ limi…
The "states-non-conserving" fermion density of states (DOS), deduced from the specific heat of hole-doped cuprates, could arise from a Kondo or heavy fermion-like DOS being suppressed by anti-ferromagnetic spin fluctuations. The large Fermi surface predicted by band theory and observed experimentally, is still expected for zero pseudogap, but with an effective mass corresponding to a Kondo temperature ~ 800 K. A finite pseudogap could divide it into Fermi arcs. Theoretical results for the asymmetric Anderson model can account for the experimental Wilson ratio.
Realizing new classes of ground states in strongly correlated electron systems continues to be at the forefront of condensed matter physics. Heavy-fermion materials, whose electronic structure is essentially three-dimensional, are one of the most suitable systems for obtaining novel electronic states because they demonstrate many fascinating properties. Recently, a state-of-the-art MBE technique has been developed to reduce the dimensionality of the heavy electrons by fabricating heavy fermion superlattices, which can produce new electronic states present in two-dimensional (2D) heavy fermion …
Magnetic impurities coupled to both fermionic and bosonic baths or to a fermionic bath with pseudogap density of states, described by the Fermi-Bose Kondo and pseudogap Kondo models, display non-trivial intermediate coupling fixed points associated with critical local-moment fluctuations and local non-Fermi liquid behavior. Based on renormalization group together with a renormalized perturbation expansion around the free-impurity limit, we calculate various impurity properties in the vicinity of those intermediate-coupling fixed points. In particular, we compute the conduction electron T matri…
Fermi surface of heavy electron systems plays a fundamental role in understanding their variety of puzzling phenomena, for example, quantum criticality, strange metal behavior, unconventional superconductivity and even enigmatic phases with yet unknown order parameters. The spectroscopy measurement of typical heavy fermion superconductor CeCoIn$_{5}$ has demonstrated multi-Fermi surface structure, which has not been in detail studied theoretically in a model system like the Kondo-Heisenberg model. In this work, we make a step toward such an issue with revisiting the Kondo-Heisenberg model. It …
The explanation of heavy-fermion superconductivity is a long-standing challenge to theory. It is commonly thought to be connected to non-local fluctuations of either spin or charge degrees of freedom and therefore of unconventional type. Here we present results for the Kondo-lattice model, a paradigmatic model to describe heavy-fermion compounds, obtained from dynamical mean-field theory which captures local correlation effects only. Unexpectedly, we find robust s-wave superconductivity in the heavy-fermion state. We argue that this novel type of pairing is tightly connected to the formation o…
Strongly correlated electron systems at the border of magnetism are of active current interest, particularly because the accompanying quantum criticality provides a route towards both strange-metal non-Fermi liquid behavior and unconventional superconductivity. Among the many important questions is whether the magnetism acts simply as a source of fluctuations in the textbook Landau framework, or instead serves as a proxy for some unexpected new physics. We put into this general context the recent developments on quantum phase transitions in antiferromagnetic heavy fermion metals. Among these a…
We report the effect of hydrostatic pressure on the resistivity of the heavy fermion Kondo lattice compound Yb$_2$Fe$_3$Si$_5$ in the temperature range 2-300 K and in pressures upto 10 Kbar. At ambient pressure the resistivity shows a prominent Kondo effect. The Kondo minimum shifts from 22.5 K at ambient pressure to 19.2 K at a pressure of 10 Kbar. The depth of the Kondo minimum also progressively decreases with pressure. These results suggest a possible weakening of the Kondo effect with the application of pressure.
The mechanism of strange metal (SM) with unconventional charge transport near magnetic phase transitions has become an outstanding open problem in correlated electron systems. Recently, an exotic quantum critical SM phase was observed in paramagnetic frustrated heavy-fermion materials near Kondo breakdown. We establish a controlled theoretical framework to this issue via a dynamical large-N fermionic multichannel approach to the two-dimensional Kondo-Heisenberg lattice model, where KB transition separates a heavy-Fermi liquid from fermionic spin-liquid state. With Kondo fluctuations being full…
We study the quantum phase transition from an antiferromagnetic metal to a heavy fermion metal in the Kondo lattice model. Based on the strong coupling approach we {\it first} diagonalize the Kondo coupling term. Since this strong coupling approach makes the resulting Kondo term {\it relevant}, the Kondo hybridization persists even in the antiferromagnetic metal, indicating that fluctuations of Kondo singlets are not critical in the phase transition. We find that the quantum transition in our strong coupling approach results from {\it softening of antiferromagnetic spin fluctuations of localiz…
Quantum criticality in certain heavy-fermion metals is believed to go beyond the Landau framework of order-parameter fluctuations. In particular, there is considerable evidence for Kondo destruction: a disappearance of the static Kondo singlet amplitude that results in a sudden reconstruction of Fermi surface across the quantum critical point and an extra critical energy scale. This effect can be analyzed in terms of a dynamical interplay between the Kondo and RKKY interactions. In the Kondo-destroyed phase, a well-defined Kondo resonance is lost, but Kondo singlet correlations remain at nonze…
We study the Kondo lattice model on the geometrically frustrated Shastry-Sutherland lattice focusing on the quantum phase transition between the valence bond solid and the heavy fermion liquid phase. By explicitly including spinon pairing of local moments at the mean-field level, we establish the emergence of a unique heavy fermion superconducting phase induced by dimer ordering of the local moments coexisting with Kondo hybridization. Furthermore, we demonstrate that for suitable choices of parameters, a partial Kondo-screening phase, where some of the valence bonds are broken, precedes the a…
Ground state properties of a Kondo lattice model with random configuration of $f$ electrons are investigated with a variational Monte Carlo method. We show that the crossover from a dilute-Kondo system to a heavy-fermion system occurs when the density of $c$ and $f$ electrons ($n_c$, $n_f$) become comparable, $n_f\lesssim n_c$. In the heavy-fermion region, the correlation between $f$ electrons is strong and the $f$ electrons themselves greatly contribute to the screening of other $f$-electron moments. We propose that the character of Kondo screening changes from "individual" to "collective" ac…
We present a mechanism of resistivity minimum in conduction electron systems coupled with localized moments, which is distinguished from the Kondo effect. Instead of the spin-flip process in the Kondo effect, electrons are elastically scattered by local spin correlations which evolve in a particular way under geometrical frustration as decreasing temperature. This is demonstrated by the cellular dynamical mean-field theory for a spin-ice type Kondo lattice model on a pyrochlore lattice. Peculiar temperature dependences of the resistivity, specific heat, and magnetic susceptibility in the non-K…
The unconventional critical behavior near magnetic quantum phase transitions in various heavy-fermion metals, apparently inconsistent with the standard spin-density-wave scenario, has triggered proposals on the breakdown of the Kondo effect at the critical point. Here we investigate, within one specific scenario, the fate of such a zero-temperature transition upon coupling of the electronic to lattice degrees of freedom. We study a Kondo-Heisenberg model with volume-dependent Kondo coupling -- this model displays both Kondo volume collapse and Kondo-breakdown transitions, as well as Lifshitz t…
Starting from the two-orbital Kondo-lattice model with classical t_2g spins, an effective spinless fermion model is derived for strong Hund coupling J_H with a projection technique. The model is studied by Monte Carlo simulations and analytically using a uniform hopping approximation. The results for the spinless fermion model are in remarkable agreement with those of the original Kondo-lattice model, independent of the carrier concentration, and even for moderate Hund coupling J_H. Phase separation, the phase diagram in uniform hopping approximation, as well as spectral properties including t…
Replacing a magnetic atom by a spinless atom in a heavy fermion compound generates a quantum state often referred to as a 'Kondo-hole'. No experimental imaging has been achieved of the atomic-scale electronic structure of a Kondo-hole, or of their destructive impact (Lawrence JM, et al. (1996) Kondo hole behavior in Ce0. 97La0. 03Pd3. Phys Rev B 53:12559-12562; Bauer ED, et al. (2011) Electronic inhomogeneity in a Kondo lattice. Proc Natl Acad Sci. 108:6857-6861) on the hybridization process between conduction and localized electrons which generates the heavy fermion state. Here we report visu…
We study the Kondo lattice model using a class of canonical transformations that allow us to faithfully represent the model entirely in terms of fermions without constraints. The transformations generate interacting theories that we study using mean field theory. Of particular interest is a new manifestly O(3)-symmetric representation in terms of Majorana fermions at half-filling on bipartite lattices. This representation suggests a natural O(3)-symmetric trial state that is investigated and characterized as a gapped spin liquid.
One of the challenges in strongly correlated electron systems, is to understand the anomalous electronic behavior that develops at an antiferromagnetic quantum critical point (QCP), a phenomenon that has been extensively studied in heavy fermion materials. Current theories have focused on the critical spin fluctuations and associated break-down of the Kondo effect. Here we argue that the abrupt change in Fermi surface volume that accompanies heavy fermion criticality leads to critical charge fluctuations. Using a model one dimensional Kondo lattice in which each moment is connected to a separa…
We study theoretically a triangular cluster of three magnetic impurities, hybridizing locally with conduction electrons of a metallic host. Such a cluster is the simplest to exhibit frustration - an important generic feature of many complex molecular systems in which different interactions compete. Here, low-energy doublet states of the trimer are favored by effective exchange interactions produced by strong electronic repulsion in localized impurity orbitals. Parity symmetry protects a level-crossing of such states on tuning microscopic parameters, while an avoided crossing arises in the gene…
The effect of Mn substitution, acting as a magnetic impurity for Fe, on the Dirac cone was investigated in Ba(Fe$_{1-x}$Mn$_x$As)$_2$. Both magnetoresistance and Hall resistivity studies clearly indicate that the cyclotron effective mass ($m^{\ast}$) of the Dirac cone is anomalously enhanced at low temperatures by the impurity, although its evolution as a function of carrier number proceeds in a conventional manner at higher temperatures. Kondo-like band renormalization induced by the magnetic impurity scattering is suggested as an explanation for this, and the anomalous mass enhancement of th…
In this study, we investigate the Kondo effect induced by the s-d interaction where the conduction bands are occupied by Dirac fermions. The Dirac fermion has the linear dispersion and is described typically by the Hamiltonian such as $H_k= v{\bf k}\cdot σ+m σ_0$ for the wave number ${\bf k}$ where $σ_j$ are Pauli matrices and $σ_0$ is the unit matrix. We derived the formula of the Kondo temperature $T_K$ by means of the Green's function theory for Green's functions including Dirac fermions and the localized spin. The $T_K$ was determined from a singularity of Green's functions in the form $T_…
We propose a two-stage spin quenching scenario for the unusual heavy fermion state realized in the mixed valent metal LiV$_2$O$_4$. In this theory, local valence fluctuations are responsible for the formation of partially quenched, spin 1/2 moments below room temperature. Frustration of the intersite spin couplings then drives the system to produce the heavy Fermi liquid seen at low temperatures. The anomalous resistivity and the sign change of the Hall constant can be understood naturally within this model, which also predicts a unique symmetry for the heavy quasiparticle bands that may be ob…
The conformal field theory (CFT) approach to Kondo problems, originally developed by Affleck and Ludwig (AL), has greatly advanced the fundamental knowledge of Kondo physics. The CFT approach to Kondo impurities is based on a necessary approximation, i.e., the linearization of the low-lying excitations in a narrow energy window about the Fermi surface. This treatment works well in normal metal baths, but encounters fundamental difficulties in systems with Fermi points and high-order dispersion relations. Prominent examples of such systems are the recently-proposed topological semimetals with e…
In this work we combine the well established Kondo problem with the more speculative field of a discrete space time. We show that a discrete energy space induces a flow towards a new fixed point by breaking the conservation of charge and spin and lifting the fermion parity. This parity lifting fixed point appears on a scale set by the discretization of energy space. In contrast to the Planck scale the associated energy scale is at very low energy scales, possibly given by the inverse size of the universe.
Kondo Echo Dynamics of Terahertz-Pumped Heavy Fermions
Physikalisches Institut and Bethe Center for Theoretical Physics, Universität Bonn（波恩大学物理研究所与贝特理论物理中心）；Institute for Quantum Computing Analytics (PGI-12), Forschungszentrum Jülich（于利希研究中心量子计算分析研究所（PGI-12））；School of Physics and Astronomy, University of St. Andrews（圣安德鲁斯大学物理与天文学学院）
Kondo insulators are primary candidates in the search for strongly correlated topological quantum phases, which may host topological order, fractionalization, and non-Abelian statistics. Within some Kondo insulators, the hybridization gap is predicted to protect a nontrivial topological invariant and to harbor emergent heavy Dirac fermion surface modes. We use high-energy-resolution spectroscopic imaging in real and momentum space on the Kondo insulator, SmB$_6$. On cooling through $T^*_Δ\approx$ 35 K we observe the opening of an insulating gap that expands to $Δ\approx$ 10 meV at 2 K. Within …
Quantum criticality beyond the Landau paradigm represents a fundamental problem in condensed matter and statistical physics. Heavy fermion systems with multipolar degrees of freedom can play an important role in the search for its universal description. We consider a Kondo lattice model with both spin and quadrupole degrees of freedom, which we show to exhibit an antiferroquadrupolar phase. Using a field theoretical representation of the model, we find that Kondo couplings are exactly marginal in the renormalization group sense in this phase. This contrasts with the relevant nature of the Kond…
Resolving the heavy fermion band in the conduction electron momentum resolved spectral function of the Kondo lattice model is challenging since, in the weak coupling limit, its spectral weight is exponentially small. In this article we consider a composite fermion operator, consisting of a conduction electron dressed by spin fluctuations that shares the same quantum numbers as the electron operator. Using approximation free auxiliary field quantum Monte Carlo simulations we show that for the SU(2) spin-symmetric model on the square lattice at half filling, the composite fermion acts as a magni…
Magnetic frustrations can enhance quantum zero-point motion in spin systems and lead to exotic topological insulating states. When coupled to mobile electrons, they may lead to unusual non-Fermi liquid or metallic spin liquid states whose nature has not been well explored. Here, we propose a spin current Kondo mechanism underlying a series of non-Fermi liquid phases on the border of Kondo and magnetic phases in a frustrated three-impurity Kondo model. This mechanism is confirmed by renormalization group analysis and describes movable Kondo singlets called "holons" induced by an effective coupl…
A spin-$\frac{1}{2}$ Kitaev sublattice interacting with a subsystem of spinless fermions is studied on a honeycomb lattice when the fermion band is half filled. The model Hamiltonian describes a topological Kondo lattice with the Kitaev interaction, it is solved exactly by reduction to free Majorana fermions in a static $\mathbb{Z}_2$ gauge field. An yet unsolved problem of a hybridization of fermions and local moments in the Kondo lattice at low temperatures is solved in the framework of the model proposed. The Kondo hybridization gap is opened and the system is fixed in insulator and spin in…
A key notion in heavy-fermion systems is the entanglement between conduction electrons and localized spin degrees of freedom. To study these systems from this point of view, we compute the mutual information in a ferromagnetic and antiferromagnetic Kondo lattice model in the presence of geometrical frustration. Here the interplay between the Kondo effect, the Ruderman-Kittel-Kasuya-Yosida interaction, and geometrical frustration leads to partial Kondo screened, conventional Kondo insulating, and antiferromagnetic phases. In each of these states the mutual information follows an area law, the c…
We investigate the Kondo effect with Wilson fermions. This is based on a mean-field approach for the chiral Gross-Neveu model including four-point interactions between a light Wilson fermion and a heavy fermion. For massless Wilson fermions, we demonstrate the appearance of the Kondo effect. We point out that there is a coexistence phase with both the light-fermion scalar condensate and Kondo condensate, and the critical chemical potentials of the scalar condensate are shifted by the Kondo effect. For negative-mass Wilson fermions, we find that the Kondo effect is favored near the parameter re…
The underlying Dirac point is central to the profound physics manifested in a wide class of materials. However, it is often difficult to drive a system with Dirac points across the massless fermionic critical point. Here by exploiting screening of local moments under spin-orbit interactions in a Kondo lattice, we show that below the Kondo temperature, the Kondo lattice undergoes a topological transition from a strong topological insulator to a weak topological insulator at a finite temperature $T_D$. At $T_D$, massless Dirac points emerge and the Kondo lattice becomes a Dirac semimetal. Our an…
