One-dimensional 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.

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.

Coupled dimer and bond-order-wave order in the quarter-filled one-dimensional Kondo lattice model

Motivated by the experiments on the organic compound $(Per)_{2}[Pt(mnt)_{2}]$, we study the ground state of the one-dimensional Kondo lattice model at quarter filling with the density matrix renormalization group method. We show a coupled dimer and bond-order-wave (BOW) state in the weak coupling regime for the localized spins and itinerant electrons, respectively. The quantum phase transitions for the dimer and the BOW orders occur at the same critical coupling parameter $J_{c}$, with the opening of a charge gap. The emergence of the combination of dimer and BOW order agrees with the experimental findings of the simultaneous Peierls and spin-Peierls transitions at low temperatures, which provides a theoretical understanding of such phase transition. We also show that the localized spins in this insulating state have quasi-long ranged spin correlations with collinear configurations, which resemble the classical dimer order in the absence of a magnetic order.

Superconducting Correlations in the One-Dimensional Kondo Lattice Models under Magnetic Fields

We analyze superconducting correlations in the one-dimensional Kondo lattice models with Ising anisotropy under transverse magnetic fields, using the density matrix renormalization group. For the spin-1/2 local spin model, the Ising anisotropy is introduced by the ferromagnetic Ising interaction between the local spins, while for the spin-1 model, it is taken by the single-ion anisotropy. The magnetic properties under the transverse fields for the spin-1/2 model are very similar to those for the spin-1 model [K. Suzuki and K. Hattori, J. Phys. Soc. Jpn. 88, 024707 (2019).]. For the superconducting correlations, we analyze various Cooper pairs within nearest-neighbor pairs including composite ones between the local spins and the electrons. We find that, for the spin-1/2 model, the superconducting correlations are highly enhanced in the Tomonaga-Luttinger liquid state near the Kondo-plateau phase, where the conduction electrons and the local spins are strongly coupled with a finite spin gap for the Ising axis. This is a clear contrast to the model under the longitudinal magnetic fields, where there are no noticeable superconducting correlations. Competitions between the transverse magnetic field and the Kondo singlet formation lead to this enhanced superconducting correlations. For the spin-1 model, the single-ion anisotropy suppresses the superconducting correlation and there is no noticeable enhancement. We also examine the large Kondo exchange coupling limit. For the moderate ferromagnetic Ising interaction between the local spins, we find that another type of superconducting correlation is enhanced inside the ferromagnetic phase. We discuss a possible relation between our results and reentrant superconductivity in U-based ferromagnetic superconductors under transverse magnetic fields.

Spin-current diode with a monoaxial chiral magnet

Monoaxial chiral magnets exhibit a chiral conical magnetic state in a magnetic field parallel to the chiral axis. The conical spins carry the potential for nonreciprocal transport phenomena, as they break both spatial inversion and time reversal symmetries. Here, we study the spin-dependent transport in the chiral conical magnetic state, using the Landauer method based on Green's functions for a one-dimensional Kondo lattice model. We show that the system exhibits nonreciprocal spin transport, which depends on the chirality, period, cone angle, and polarization of the spin current. In particular, we find the distinct cone angle dependence between the spin textures with long and short periods. We also show that the nonreciprocity is related to the spin states of itinerant electrons near the leads. Our results indicate that the chiral cone acts as a spin-current diode, which can be flexibly controlled by a magnetic field.

Ground-State Phase Diagram of theS= 1 One-Dimensional Kondo Lattice Model with a Uniaxial Anisotropy under Transverse Fields

We study the effects of transverse magnetic fields on the $S=1$ one-dimensional Kondo lattice model with a uniaxial anisotropy using the density matrix renormalization group. The model can be regarded as a simplified one for analyzing the Ising ferromagnetic superconductor URhGe. We find various phases such as ferromagnetic and antiferromagnetic phases, Kondo plateau (KP) phases, Tomonaga-Luttinger liquids, and fully polarized phases. In the KP phase, a pseudoplateau emerges in the magnetization due to strongly bound pairs between the local and the conduction electron spins. This is why we call this phase the Kondo plateau. At the critical field between the ferromagnetic and KP phases, we find metamagnetic behavior in the magnetization curve. We discuss various correlation functions and the Friedel oscillations in detail, and the experimental data under transverse magnetic fields in URhGe are discussed on the basis of the present results.

Chiral helimagnetic state in a Kondo lattice model with the Dzyaloshinskii–Moriya interaction

Monoaxial chiral magnets can form a noncollinear twisted spin structure called the chiral helimagnetic state. We study magnetic properties of such a chiral helimagnetic state, with emphasis on the effect of itinerant electrons. Modeling a monoaxial chiral helimagnet by a one-dimensional Kondo lattice model with the Dzyaloshinskii–Moriya interaction, we perform a variational calculation to elucidate the stable spin configuration in the ground state. We obtain a chiral helimagnetic state as a candidate for the ground state, whose helical pitch is modulated by the model parameters: the Kondo coupling, the Dzyaloshinski–Moriya interaction, and electron filling.

Monte Carlo Study of Magnetoresistance in a Chiral Soliton Lattice

Monoaxial chiral magnets can form a peculiar noncollinear spin structure called the chiral soliton lattice in an applied magnetic field perpendicular to the helical axis. We study magnetic properties and electrical transport in the chiral soliton lattice by a Monte Carlo simulation for a one-dimensional Kondo lattice model including the Dzyaloshinskii-Moriya interaction between classical localized spins. We show that the model exhibits a helical spin structure at a zero magnetic field, which turns into the chiral soliton lattice, and finally, to a forced ferromagnetic state with increasing the external magnetic field. In the chiral soliton lattice state, we find negative magnetoresistance proportional to the number of solitons at low temperature, which corroborates the spin scattering of electrons by chiral solitons. We also discuss the temperature and magnetic field dependence of the spin structure factor and electrical resistivity, in comparison with experiments for CrNb$_{3}$S$_{6}$.

Low-Temperature Magnetic Properties of the Kondo Lattice Model in One Dimension

Low-temperature magnetic properties of the one-dimensional Kondo-lattice model with classical localized spins are investigated by means of a Monte Carlo simulation combined with an exact diagonalization technique. Comparative simulations are also made for the RKKY classical Heisenberg model known to be perturbatively derived in the weak-coupling limit. In addition to the previously identified antiferromagnetic, ferromagnetic and coplanar helical phases, the chiral noncoplanar phase and the collinear phases of the period-4 and 6 are newly identified, neither of which is realized in the corresponding RKKY model. The period-4 collinear phase persists even in the weak-coupling limit at the 1/4- and 3/4-fillings, invalidating the perturbative approach at these fillings.

Ferromagnetic state in the one-dimensional Kondo lattice model

In our recent study [Phys. Rev. Lett. 108, 086402 (2012)], we revealed the intriguing properties of the ferromagnetic state in the Kondo lattice model with antiferromagnetic coupling in infinite dimensions: within the ferromagnetic metallic phase, the minority conduction electrons form a gap at the Fermi energy and do not participate in transport, irrespective of interaction strength and filling. This half-metallic state is referred to as a spin-selective Kondo insulator. Here we show that the spin-selective Kondo insulator can also be realized in the one-dimensional Kondo lattice model by studying static and dynamical quantities with the density-matrix renormalization group. The emergence of the spin-selective Kondo insulator, both in one and infinite dimensions, certainly demonstrates that this mechanism is quite general and ubiquitous for the ferromagnetic state in the Kondo lattice model, irrespective of the dimensionality of the system.

Coulomb interaction effects and electron spin relaxation in the one-dimensional Kondo lattice model

We study the effects of the Coulomb interaction in the one dimensional Kondo lattice model on the phase diagram, the static magnetic susceptibility and electron spin relaxation. We show that onsite Coulomb interaction supports ferromagnetic order and nearest neighbor Coulomb interaction drives, depending on the electron filling, either a paramagnetic or ferromagnetic order. Furthermore we calculate electron quasiparticle life times, which can be related to electron spin relaxation and decoherence times, and explain their dependence on the strength of interactions and the electron filling in order to find the sweet spot of parameters where the relaxation time is maximized. We find that effective exchange processes between the electrons dominate the spin relaxation and decoherence rate.

Quasiparticles in the Kondo lattice model at partial fillings of the conduction band using the density matrix renormalization group

We study the spectral properties of the one-dimensional Kondo lattice model as a function of the exchange coupling, the band filling, and the quasimomentum in the ferromagnetic and paramagnetic phases. Using the density-matrix renormalization group method, we compute the dispersion relation of the quasiparticles, their lifetimes, and the $Z$ factor. Sigrist et al. [Phys. Rev. Lett. 67, 2211 (1991)] provided the exact ground state and the quasiparticle-dispersion relation of the Kondo lattice model with one conduction electron. The quasiparticle could be identified as the spin polaron. Our calculations of the dispersion relation for partial band fillings give a result similar to the one-electron case, which suggests that the quasiparticle in both cases is the spin polaron. We find that the quasiparticle lifetime differs by orders of magnitude between the ferromagnetic and paramagnetic phases and depends strongly on the quasimomentum.

One-dimensional Kondo lattice model at quarter filling

We revisit the problem of the quarter-filled one-dimensional Kondo lattice model, for which the existence of a dimerized phase and a nonzero charge gap had been reported by Xavier et al. [Phys. Rev. Lett. 90, 247204 (2003)]. Recently, some objections were raised claiming that the system is neither dimerized nor has a charge gap. In the interest of clarifying this important issue, we show that these objections are based on results obtained under conditions in which the dimer order is artificially suppressed. We use the incontrovertible dimerized phase of the Majumdar-Ghosh point of the ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model as a paradigm with which to illustrate this artificial suppression. Finally, by means of extremely accurate density-matrix renormalization-group calculations, we show that the charge gap is indeed nonzero in the dimerized phase.

One-dimensional Kondo lattice model studied through numerical diagonalization

The one-dimensional Kondo lattice model is studied by means of the numerical diagonalization method. By using massively parallel computations, we were able to study lattices large enough to obtain convergent results for electron densities $n\ensuremath{\leqslant}2∕3$. For such densities, an additional ferromagnetic region is found inside the paramagnetic phase. Also, a region is found where the localized spins participate in the low-energy dynamics together with the conduction electrons, thus resulting in a large Fermi surface. These results are an independent confirmation of previous density matrix renormalization group results.

Magnetic and transport properties of the one-dimensional ferromagnetic Kondo lattice model with an impurity

We have studied the ferromagnetic Kondo lattice model (FKLM) with an Anderson impurity on finite chains with numerical techniques. We are particularly interested in the metallic ferromagnetic phase of the FKLM. This model could describe either a quantum dot coupled to one-dimensional ferromagnetic leads made with manganites or a substitutional transition metal impurity in a MnO chain. We determined the region in parameter space where the impurity is empty, half filled, or doubly occupied and, hence, where it is magnetic or nonmagnetic. The most important result is that we found, for a wide range of impurity parameters and electron densities where the impurity is magnetic, a singlet phase located between two saturated ferromagnetic phases which correspond approximately to the empty and doubly occupied impurity states. Transport properties behave, in general, as expected as a function of the impurity occupancy, and they provide a test for a recently developed numerical approach to compute the conductance. The results obtained could be, in principle, reproduced experimentally in already existent related nanoscopic devices or in impurity doped MnO nanotubes.

Flow equations for the one-dimensional Kondo lattice model: static and dynamic ground state properties

The one-dimensional Kondo lattice model is investigated by means of Wegner's flow equation method. The renormalization procedure leads to an effective Hamiltonian which describes a free one-dimensional electron gas and a Heisenberg chain. The localised spins of the effective model are coupled by the well-known RKKY interaction. They are treated within a Schwinger boson mean field theory which permits the calculation of static and dynamic correlation functions. In the regime of small interaction strength static expectation values agree well with the expected Luttinger liquid behaviour. The parameter K_rho of the Luttinger liquid theory is estimated and compared to recent results from density matrix renormalization group studies.

Absence of dimer order and the Tomonaga–Luttinger liquid properties of the quarter-filled one-dimensional Kondo-lattice model

A novel spin dimer order is recently reported in the ground state of the one-dimensional Kondo lattice model at quarter-filling. Being dubious about such long-range order in the absence of a spin gap, we perform the density matrix renormalization group calculation at under several boundary conditions. It turns out that dimer spin structure is sensitive to the boundary conditions, and that the dimer correlation function decays in small power law at long distances, indicating the absence of dimer long-range order. This together with a possible absence of charge gap suggests that the true ground state remains to be a Tomonaga–Luttinger liquid with small K ρ .

Local spin order in one-dimensional Kondo lattice model for band fillingn=1∕3

The local spin order in the one-dimensional Kondo lattice model is studied for the conduction-electron band filling $n=\frac{1}{3}$ in a special parameter case. The charge and spin gaps are calculated. We obtain two phases. One is the local spin island phase with spin and charge gap in the conduction band. In another phase, the local spins order antiferromagnetically and there is spin gap. Between these two phases, there is a first order transition.

Static spin configuration in the one-dimensional Kondo lattice model

The local spin order in the one-dimensional Kondo lattice model is studied for the conduction-electron band filling $n=\frac{1}{2}$ and $\frac{1}{3}$ in a special parameter case. The local spin-dimerization ground state is confirmed for the quarter-filling case. And the spin order is studied for $n=\frac{1}{3}$. The spin and charge gaps are given for different band-filling cases.

The one-dimensional Kondo lattice model at partial band filling

The Kondo lattice model introduced in 1977 describes a lattice of localized magnetic moments interacting with a sea of conduction electrons. It is one of the most important canonical models in the study of a class of rare earth compounds, called heavy fermion systems, and as such has been studied intensively by a wide variety of techniques for more than a quarter of a century. This review focuses on the one dimensional case at partial band filling, in which the number of conduction electrons is less than the number of localized moments. The theoretical understanding, based on the bosonized solution, of the conventional Kondo lattice model is presented in great detail. This review divides naturally into two parts, the first relating to the description of the formalism, and the second to its application. After an all-inclusive description of the bosonization technique, the bosonized form of the Kondo lattice hamiltonian is constructed in detail. Next the double-exchange ordering, Kondo singlet formation, the RKKY interaction and spin polaron formation are described comprehensively. An in-depth analysis of the phase diagram follows, with special emphasis on the destruction of the ferromagnetic phase by spin-flip disorder scattering, and of recent numerical results. The results are shown to hold for both antiferromagnetic and ferromagnetic Kondo lattice. The general exposition is pedagogic in tone.