Kondo Lattice Model Research Articles

Numerical signatures of ultra-local criticality in a one dimensional Kondo lattice model

Heavy fermion criticality has been a long-standing problem in condensed matter physics. Here we study a one-dimensional Kondo lattice model through numerical simulation and observe signatures of local criticality. We vary the Kondo coupling J_KJK at fixed doping x. At large positive J_KJK, we confirm the expected conventional Luttinger liquid phase with 2k_F=\frac{1+x}{2}2kF=1+x2 (in units of 2\pi2π), an analogue of the heavy Fermi liquid (HFL) in the higher dimension. In the J_K ≤ 0JK≤0 side, our simulation finds the existence of a fractional Luttinger liquid (LL\star⋆) phase with 2k_F=\frac{x}{2}2kF=x2, accompanied by a gapless spin mode originating from localized spin moments, which serves as an analogue of the fractional Fermi liquid (FL\star⋆) phase in higher dimensions. The LL\star⋆ phase becomes unstable and transitions to a spin-gapped Luther-Emery (LE) liquid phase at small positive J_KJK. Then we mainly focus on the “critical regime” between the LE phase and the LL phase. Approaching the critical point from the spin-gapped LE phase, we often find that the spin gap vanishes continuously, while the spin-spin correlation length in real space stays finite and small. For a certain range of doping, in a point (or narrow region) of J_KJK, the dynamical spin structure factor obtained through the time-evolving block decimation (TEBD) simulation shows dispersion-less spin fluctuations in a finite range of momentum space above a small energy scale (around 0.035 J0.035J) that is limited by the TEBD accuracy. All of these results are unexpected for a regular gapless phase (or critical point) described by conformal field theory (CFT). Instead, they are more consistent with exotic ultra-local criticality with an infinite dynamical exponent z=+z=+. The numerical discovery here may have important implications on our general theoretical understanding of the strange metals in heavy fermion systems. Lastly, we propose to simulate the model in a bilayer optical lattice with a potential difference.

Emergence and evolution of electronic modes with temperature in spin-gapped Mott and Kondo insulators

Electronic modes emerge within the band gap at nonzero temperature in strongly correlated insulators such as Mott and Kondo insulators, exhibiting momentum-shifted magnetic dispersion relations from the band edges. As the temperature increases, the emergent modes gain considerable spectral weights and form robust bands that differ from the zero-temperature bands. Here, the origin of the emergent modes, their relation to doping-induced modes, and how their spectral weights increase with temperature are clarified in the ladder and bilayer Hubbard models and one- and two-dimensional Kondo lattice models using effective theory for weak inter-unit-cell hopping and numerical calculations. The results indicate that the temperature-driven change in the band structure reflecting spin excitation, including the change in the number of bands, can be observed in various strongly correlated insulators even with a spin gap, provided that the temperature increases up to about spin-excitation energies. The controlled analyses developed in this study significantly contribute to the fundamental understanding of the band structure of strongly correlated insulators at nonzero temperature. Published by the American Physical Society 2024

Many-body Chern insulator in the Kondo lattice model on a triangular lattice

Many-body Chern insulator in the Kondo lattice model on a triangular lattice

Theory of Collective Excitations in the Quadruple-Q Magnetic Hedgehog Lattices.

Hedgehog and antihedgehog spin textures in magnets behave as emergent monopoles and antimonopoles, which give rise to astonishing transport and electromagnetic phenomena. Using the Kondo-lattice model in three dimensions, we theoretically study collective spin-wave excitation modes of magnetic hedgehog lattices which have recently been discovered in itinerant magnets such as MnSi_{1-x}Ge_{x} and SrFeO_{3}. It is revealed that the spin-wave modes, which appear in the subterahertz regime, have dominant amplitudes localized at Dirac strings connecting hedgehog-antihedgehog pairs and are characterized by their translational oscillations. It is found that their spectral features sensitively depend on the number and configuration of the Dirac strings and, thus, can be exploited for identifying the topological phase transitions associated with the monopole-antimonopole pair annihilations.

A microscopic view of checkerboard and striped charge orders through doping antiferromagnetic Mott insulator

The emergence of charge order in doped Mott insulators has received considerable attention due to its relevance to a variety of realistic materials and experiments. To investigate the interplay between magnetic and charge order, we have studied the semiclassical Kondo lattice model, which includes both electronic and magnetic degrees of freedom. By combining Langevin dynamical simulations with the kernel polynomial method, our results reveal the presence of charged stripe order, checkerboard order, and non-uniform charge disorder in the near-half-filling regime. Importantly, our simulations show that both the doping level and the strength of the s-d exchange coupling play a crucial role in facilitating charge order formation. These phases give rise to distinct electronic structures as well as excitations in the magnetic dynamics, providing insights into the underlying mechanism of charge ordering phenomena.

Dynamic mass generation and topological order in overscreened Kondo lattices

Multichannel Kondo lattice models are examples of strongly correlated electronic systems that exhibit non-Fermi-liquid behavior due to the presence of a continuous channel symmetry. Mean-field analyses have predicted that these systems undergo channel symmetry breaking at low temperature. We use the dynamical large-N technique to study temporal and spatial fluctuations of the multichannel Kondo model on a honeycomb lattice and find that this prediction is not generally true. Rather, we find a (2+1)-dimensional conformally invariant fixed point, governed by critical exponents that are found numerically. When we break time-reversal symmetry by adding a Haldane mass to the conduction electrons, three phases, separated by continuous transitions, are discernible: one characterized by dynamic mass generation and spontaneous breaking of the channel symmetry, one where topological defects restore channel symmetry but preserve the gap, and one with a Kondo-coupled chiral spin liquid. We argue that the last phase is a fractional Chern insulator with anyonic excitations. Published by the American Physical Society 2024

Nature of the Unconventional Heavy-Fermion Kondo State in Monolayer CeSiI.

CeSiI has been recently isolated in the ultrathin limit, establishing CeSiI as the first intrinsic two-dimensional van der Waals heavy-fermion material up to 85 K. We show that, due to the strong spin-orbit coupling, the local moments develop a multipolar real-space magnetic texture, leading to local pseudospins with a nearly vanishing net moment. To elucidate its Kondo-screened regime, we extract from first-principles the parameters of the Kondo lattice model describing this material. We develop a pseudofermion methodology in combination with ab initio calculations to reveal the nature of the heavy-fermion state in CeSiI. We analyze the competing magnetic interactions leading to an unconventional heavy-fermion order as a function of the magnetic exchange between the localized f-electrons and the strength of the Kondo coupling. Our results show that the magnetic exchange interactions promote an unconventional momentum-dependent Kondo-screened phase, establishing the nature of the heavy-fermion state observed in CeSiI.

Charge-density wave mediated quasi-one-dimensional Kondo lattice in stripe-phase monolayer 1T-NbSe2

The heavy fermion physics is dictated by subtle competing exchange interactions, posing a challenge to their understanding. One-dimensional (1D) Kondo lattice model has attracted special attention in theory, because of its exact solvability and expected unusual quantum criticality. However, such experimental material systems are extremely rare. Here, we demonstrate the realization of quasi-1D Kondo lattice behavior in a monolayer van der Waals crystal NbSe2, that is driven into a stripe phase via Se-deficient line defects. Spectroscopic imaging scanning tunneling microscopy measurements and first-principles calculations indicate that the stripe-phase NbSe2 undergoes a novel charge-density wave transition, creating a matrix of local magnetic moments. The Kondo lattice behavior is manifested as a Fano resonance at the Fermi energy that prevails the entire film with a high Kondo temperature. Importantly, coherent Kondo screening occurs only in the direction of the stripes. Upon approaching defects, the Fano resonance exhibits prominent spatial 1D oscillations along the stripe direction, reminiscent of Kondo holes in a quasi-1D Kondo lattice. Our findings provide a platform for exploring anisotropic Kondo lattice behavior in the monolayer limit.

A microscopic Kondo lattice model for the heavy fermion antiferromagnet CeIn3

Electrons at the border of localization generate exotic states of matter across all classes of strongly correlated electron materials and many other quantum materials with emergent functionality. Heavy electron metals are a model example, in which magnetic interactions arise from the opposing limits of localized and itinerant electrons. This remarkable duality is intimately related to the emergence of a plethora of novel quantum matter states such as unconventional superconductivity, electronic-nematic states, hidden order and most recently topological states of matter such as topological Kondo insulators and Kondo semimetals and putative chiral superconductors. The outstanding challenge is that the archetypal Kondo lattice model that captures the underlying electronic dichotomy is notoriously difficult to solve for real materials. Here we show, using the prototypical strongly-correlated antiferromagnet CeIn3, that a multi-orbital periodic Anderson model embedded with input from ab initio bandstructure calculations can be reduced to a simple Kondo-Heisenberg model, which captures the magnetic interactions quantitatively. We validate this tractable Hamiltonian via high-resolution neutron spectroscopy that reproduces accurately the magnetic soft modes in CeIn3, which are believed to mediate unconventional superconductivity. Our study paves the way for a quantitative understanding of metallic quantum states such as unconventional superconductivity.

Machine learning assisted derivation of minimal low-energy models for metallic magnets

We consider the problem of extracting a low-energy spin Hamiltonian from a triangular Kondo Lattice Model (KLM). The non-analytic dependence of the effective spin-spin interactions on the Kondo exchange excludes the use of perturbation theory beyond the second order. We then introduce a Machine Learning (ML) assisted protocol to extract effective two- and four-spin interactions. The resulting spin model reproduces the phase diagram of the original KLM as a function of magnetic field and single-ion anisotropy and reveals the effective four-spin interactions that stabilize the field-induced skyrmion crystal phase. Moreover, this model enables the computation of static and dynamical properties with a much lower numerical cost relative to the original KLM. A comparison of the dynamical spin structure factor in the fully polarized phase computed with both models reveals a good agreement for the magnon dispersion even though this information was not included in the training data set.

Skyrmion crystals in the triangular Kondo lattice model

We present a systematic study of the formation of skyrmion crystals in a triangular Kondo Lattice model for generic electron filling fractions. Our results indicate that the four-sublattice chiral antiferromagnetic ordering that was reported more than one decade ago can be understood as the dense limit of a sequence of skyrmion crystals whose lattice parameter is dictated by the Fermi wave-vector. This observation has important implications for the ongoing search of skyrmion crystals in metallic materials with localized magnetic moments.

Equivariant neural networks for spin dynamics simulations of itinerant magnets

I present a novel equivariant neural network architecture for the large-scale spin dynamics simulation of the Kondo lattice model. This neural network mainly consists of tensor-product-based convolution layers and ensures two equivariances: translations of the lattice and rotations of the spins. I implement equivariant neural networks for two Kondo lattice models on two-dimensional square and triangular lattices, and perform training and validation. In the equivariant model for the square lattice, the validation error (based on root mean squared error) is reduced to less than one-third compared to a model using invariant descriptors as inputs. Furthermore, I demonstrate the ability to simulate phase transitions of skyrmion crystals in the triangular lattice, by performing dynamics simulations using the trained model.

Flat-band ferromagnetism in the SU(N) Hubbard and Kondo lattice models

We develop a general theory of flat-band ferromagnetism in the SU(N) Fermi–Hubbard model, which describes the behavior of N-component fermions with SU(N) symmetric interactions. We focus on the case where the single-particle spectrum has a flat band at the bottom and establish a necessary and sufficient condition for the SU(N) Hubbard model to exhibit ferromagnetism when the number of particles is the same as the degeneracy. We show that the occurrence of ferromagnetism is equivalent to the irreducibility of the projection matrix onto the space of single-particle ground states. We also demonstrate that this result can be exploited to establish a rigorous result for the ferromagnetic SU(N) Kondo lattice model with a flat band. Specifically, we prove that when the SU(N) Hubbard model is ferromagnetic, the ferromagnetic SU(N) Kondo lattice model with the same hopping matrix also exhibits SU(N) ferromagnetism.

Metamagnetic transition in the two f orbitals Kondo lattice model

In this work, we study the effects of a transverse magnetic field in a Kondo lattice model with two f orbitals interacting with the conduction electrons. The f electrons that are present on the same site interact through Hund’s coupling, while on neighboring sites they interact through intersite exchange. We consider here that part of f electrons are localized (orbital 1) while another part (orbital 2) are delocalized, as it is frequent in uranium systems. Then, only electrons in the localized orbital 1 interact through exchange interaction with the neighboring ones, while electrons in orbital 2 are coupled with conduction electrons through a Kondo interaction. We obtain a solution where ferromagnetism and Kondo effect coexist for small values of an applied transverse magnetic field for . Increasing the transverse field, two situations can be obtained when Kondo coupling vanishes: first, a metamagnetic transition occurs just before or at the same time of the fully polarized state, and second, a metamagnetic transition occurs when the spins are already pointing out along the magnetic field.

Doniach phase diagram for the Kondo lattice model on square and triangular lattices

Doniach phase diagram for the Kondo lattice model on square and triangular lattices

Kondo Lattice Model in Magic-Angle Twisted Bilayer Graphene.

We systematically study emergent Kondo lattice models from magic-angle twisted bilayer graphene using the topological heavy fermion representation. At the commensurate fillings, we demonstrate a series of symmetric strongly correlated metallic states driven by the hybridization between a triangular lattice of SU(8) local moments and delocalized fermions. In particular, a (fragile) topological Dirac Kondo semimetal can be realized, providing a potential explanation for the symmetry-preserving correlated state at ν=0. We further investigate the stability of the Dirac Kondo semimetal by constructing a quantum phase diagram showing the interplay between Kondo hybridization and magnetic correlation. The destruction of Kondo hybridization suggests that the magic-angle twisted bilayer graphene may be on the verge of a solid-state quantum simulator for novel magnetic orders on a triangular lattice. Experimental implications are also discussed.

Skyrmion crystal phases in Kondo lattice model on triangular lattices

Very often the magnetic skyrmions (topologically protected spin textures) form a triangular crystal in chiral magnets. Here we study the effect of itinerant electrons on the structure of skyrmion crystal (SkX) on triangular lattice using Kondo lattice model in the large coupling limit and treating the localized spins as classical vectors. To simulate the system, we employ hybrid Markov Chain Monte Carlo method (hMCMC) which includes electron diagonalization in each MCMC update for classical spins. We present the low-temperature results for system at electron density which show a sudden jump in skyrmion number reducing the size of the skyrmions when we increase the hopping strength of the itinerant electrons. We find that this high skyrmion number SkX phase is stabilized by a combined effect: lowering of density of states at electron filling and also pushing the bottom energy states further down. We show that these results hold for larger system using traveling cluster variation of hMCMC. We expect that itinerant triangular magnets might exhibit the possible transition between low-density to high-density SkX phases by applying external pressure.

Layer-dependent correlated phases in WSe2/MoS2 moiré superlattice.

Electron correlation plays an essential role in the macroscopic quantum phenomena in the moiré heterostructure, such as antiferromagnetism and correlated insulating phases. Unlike the phenomena where the interaction involves only electrons in one layer, the interaction of distinct phases in two or more layers represents a new horizon forward, such as the one in the Kondo lattice model. Here, using interlayer excitons as a probe, we show that the interlayer interactions in heterobilayers of tungsten diselenide and molybdenum disulfide (WSe2/MoS2) can be electrically switched on and off, resulting in a layer-dependent correlated phase diagram, including single-layer, layer-selective, excitonic-insulator and layer-hybridized regions. We demonstrate that these correlated phases affect the interlayer exciton non-radiative decay pathways. These results reveal the role of strong correlation on interlayer exciton dynamics and pave the way for studying the layer-resolved strong correlation behaviour in moiré heterostructures.

Low-frequency spin dynamics in diluted magnetic semiconductors

The low-frequency dynamical magnetic properties in paramagnetic diluted magnetic semiconductors are addressed in the framework of the dynamical mean-field theory applied for the Kondo lattice model. In the infinite-dimensional limit, a set of self-consistent equations is derived so the single-particle Green's function and its self-energy can be evaluated numerically. In terms of the Green's function and self-energies, the local dynamical spin susceptibility function and then the spin-relaxation rate are explicitly expressed based on the Baym-Kadanoff approach. It is found that the spin fluctuations become dominated, indicated by the sharp peak appearing at the low frequency of the spin dynamical susceptibility function in the case of large magnetic coupling and temperature close to the paramagnetic-ferromagnetic transition point. The low-frequency spin dynamic in the systems is also addressed in the signatures of the spin-relaxation process. In the case of large temperature and small magnetic coupling, the spin-relaxation rate releases the scenario of the Korringa process specifying the weak correlation systems likely normal metals. Otherwise, i.e., at small temperature and large magnetic coupling, we find exponential behavior of the spin-relaxation rate versus temperature. Moreover, at a temperature approaching the paramagnetic-ferromagnetic transition point, one finds sharp suppression of the spin-relaxation rate or speeding up of the spin-relaxation time. These scenarios are attributed to the appearance of the magnetic coherence bound state or the spin clusters in diluted magnetic semiconductors due to the strongly magnetic correlations.

Triplet Pairing Mechanisms from Hund's-Kondo Models: Applications to UTe_{2} and CeRh_{2}As_{2}.

Observing that several U and Ce based candidate triplet superconductors share a common structural motif, with pairs of magnetic atoms separated by an inversion center, we hypothesize a triplet pairing mechanism based on an interplay of Hund's and Kondo interactions that is unique to this structure. In the presence of Hund's interactions, valence fluctuations generate a triplet superexchange between electrons and local moments. The offset from the center of symmetry allows spin-triplet pairs formed by the resulting Kondo effect to delocalize onto the Fermi surface, precipitating superconductivity. We demonstrate this mechanism within a minimal two-channel Kondo lattice model and present support for this pairing mechanism from existing experiments.