Half-filled Kondo Lattice Research Articles

Low-temperature theory of inversion and quantum oscillations in Kondo insulators

The half-filled Kondo lattice model is studied at low temperatures on a simple cubic lattice using the self-consistent theory developed by Ram and Kumar [Phys. Rev. B 96, 075115 (2017)]. It is found to have three distinct insulating phases in the temperature-hopping plane, namely, the strong-coupling Kondo singlet (KS) phase, the inverted Kondo singlet (iKS) phase distinguished from the KS by inversion, and the antiferromagnetic (AFM) phase. The quasiparticle density of states across the inversion transition is noted to exhibit a dimensional reduction, which can differentiate between the KS and iKS insulators in experiments. Magnetic quantum oscillations obtained in the iKS and AFM phases are found to show a Lifshitz-Kosevich-like behavior with temperature as well as quantum fluctuations induced by the Kondo interaction.

Breakdown of heavy quasiparticles in a honeycomb Kondo lattice: A quantum Monte Carlo study

We show that for the half-filled Kondo lattice model on the honeycomb lattice a Kondo breakdown occurs at small Kondo couplings $J_k$ within the magnetically ordered phase. Our conclusions are based on auxiliary field quantum Monte Carlo simulations of the so-called composite fermion spectral function. Within a U(1) gauge theory formulation of the Kondo model, it becomes apparent that a Higgs mechanism dictates the weight of the resonance in the spectral function. For the honeycomb lattice we observe that for small $J_k$ the quasiparticle pole gives way to incoherent spectral weight but it remains well defined for the square lattice. Our result provides an explicit example where the magnetic transition and the breakdown of heavy quasiparticles are detached as observed in Yb(Rh$_{0.93}$Co$_{0.07}$)$_2$Si$_2$ [Friedemann et al., Nat. Phys. \textbf{5}, 465 (2009)].

Global phase diagram and momentum distribution of single-particle excitations in Kondo insulators

Kondo insulators are emerging as a simplified setting to study both magnetic and metal-to-insulator quantum phase transitions. Here, we study a half-filled Kondo lattice model defined on a magnetically frustrated Shastry-Sutherland geometry. We determine a "global" phase diagram that features a variety of zero-temperature phases; these include Kondo-destroyed antiferromagnetic and paramagnetic metallic phases in addition to the Kondo-insulator phase. Our result provides the theoretical basis for understanding how applying pressure to a Kondo insulator can close its hybridization gap, liberate the local-moment spins from the conduction electrons, and lead to a magnetically correlated metal. We also study the momentum distribution of the single-particle excitations in the Kondo insulating state, and illustrate how Fermi-surface-like features emerge as a precursor to the actual Fermi surfaces of the Kondo-destroyed metals. We discuss the implications of our results for Kondo insulators including SmB$_6$.

Quantum MonteCarlo Simulation of Frustrated Kondo Lattice Models.

The absence of the negative sign problem in quantum MonteCarlo 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 symmetry. For negative-sign-free spin and fermionic systems, we show that one can formulate a negative-sign-free auxiliary field quantum MonteCarlo 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 geometric frustration. In addition to the conventional Kondo insulator and antiferromagnetically ordered phases, we find a partial Kondo screened state where spins are selectively screened so as to alleviate frustration, and the lattice rotation symmetry is broken nematically.

Strong coupling Kondo lattice model as a Fermi gas

The strong coupling half-filled Kondo lattice model is an important example of a strongly interacting dense Fermi system for which conventional Fermi gas analysis has thus far failed. We remedy this by deriving an exact transformation that maps the model to a dilute gas of weakly interacting electron and hole quasiparticles that can then be analyzed by conventional dilute Fermi gas methods. The quasiparticle vacuum is a singlet Mott insulator for which the quasiparticle dynamics are simple. Since the transformation is exact, the electron spectral weight sum rules are obeyed exactly. Subtleties in understanding the behavior of electrons in the singlet Mott insulator can be reduced to a fairly complicated but precise relation between quasiparticles and bare electrons. The theory of free quasiparticles can be interpreted as an exactly solvable model for a singlet Mott insulator, providing an exact model in which to explore the strong coupling regime of a singlet Kondo insulator.

Coherence scale of the two-dimensional Kondo lattice model

A doped hole in the two-dimensional half-filled Kondo lattice model with exchange $J$ and hopping $t$ has momentum $(\ensuremath{\pi},\ensuremath{\pi})$ irrespective of the coupling $J∕t$. The quasiparticle residue of the doped hole, ${Z}_{(\ensuremath{\pi},\ensuremath{\pi})}$, tracks the Kondo scale, ${T}_{K}$, of the corresponding single impurity model. Those results stem from high precision quantum Monte Carlo simulations on lattices up to $12\ifmmode\times\else\texttimes\fi{}12$. Accounting for small dopings away from half-filling within a rigid band approximation, this result implies that the effective mass of the charge carriers at the Fermi level tracks $1∕{T}_{K}$ or equivalently that the coherence temperature ${T}_{\mathrm{coh}}\ensuremath{\propto}{T}_{K}$. This results is consistent with the large-N saddle point of the $SU(N)$ symmetric Kondo lattice model.

Thermodynamics of the half-filled Kondo lattice model around the atomic limit

We present a perturbation theory for studying thermodynamic properties of the Kondo spin liquid phase of the half-filled Kondo lattice model. The grand partition function is derived to calculate chemical potential, spin and charge susceptibilities and specific heat. The treatment is applicable to the model with strong couplings in any dimensions (one, two and three dimensions). The chemical potential equals zero at any temperatures, satisfying the requirement of the particle-hole symmetry. Thermally activated behaviors of the spin(charge) susceptibility due to the spin(quasiparticle) gap can be seen and the two-peak structure of the specific heat is obtained. The same treatment to the periodic Anderson model around atomic limit is also briefly discussed.

Bond-operator mean-field theory of the half-filled Kondo lattice model

We present a bond-operator mean field theory for the Kondo lattice model at half filling in two (2D) and three (3D) dimensions. A continuous quantum phase transition from an antiferromagnetic to a spin-gapped singlet ground state is found at J/t=1.505 (1.833) in 2D (3D). Additionally we evaluate the quasiparticle dispersions as well as the staggered magnetic moment and provide a comparison with complementary numerical approaches.

Spin and charge dynamics of the ferromagnetic and antiferromagnetic two-dimensional half-filled Kondo lattice model

We present a detailed numerical study of ground state and finite temperature spin and charge dynamics of the two-dimensional Kondo lattice model with hopping t and exchange J. Our numerical results stem from auxiliary field quantum Monte Carlo simulations formulated in such a way that the sign problem is absent at half-band filling thus allowing us to reach lattice sizes up to $12\ifmmode\times\else\texttimes\fi{}12.$ At $T=0$ and antiferromagnetic couplings $J>0$ the competition between the Ruderman-Kittel-Kasuya-Yosida interaction and the Kondo effect triggers a quantum phase transition between antiferromagnetically ordered and magnetically disordered insulators: ${J}_{c}/t=1.45\ifmmode\pm\else\textpm\fi{}0.05.$ At $J<0$ the system remains an antiferromagnetically ordered insulator and irrespective of the sign of J, the quasiparticle gap scales as $|J|.$ The dynamical spin structure factor $S(\stackrel{\ensuremath{\rightarrow}}{q},\ensuremath{\omega})$ evolves smoothly from its strong-coupling form with spin gap at $\stackrel{\ensuremath{\rightarrow}}{q}=(\ensuremath{\pi},\ensuremath{\pi})$ to a spin-wave form. For $J>0,$ the single-particle spectral function $A(\stackrel{\ensuremath{\rightarrow}}{k},\ensuremath{\omega})$ shows a dispersion relation following that of hybridized bands as obtained in the noninteracting periodic Anderson model. In the ordered phase this feature is supplemented by shadows, thus allowing an interpretation in terms of the coexistence of Kondo screening and magnetic ordering. In contrast, at $J<0$ the single-particle dispersion relation follows that of noninteracting electrons in a staggered external magnetic field. At finite temperatures spin ${T}_{S}$ and charge ${T}_{C}$ scales are defined by locating the maximum in the charge and spin uniform susceptibilities. For weak to intermediate couplings, ${T}_{S}$ marks the onset of antiferromagnetic fluctuations---as observed by a growth of the staggered spin susceptibility---and follows a ${J}^{2}$ law. At strong couplings ${T}_{S}$ scales as J. On the other hand ${T}_{C}$ scales as J both in the weak- and strong-coupling regime. At and slightly below ${T}_{C}$ we observe (i) the onset of screening of the magnetic impurities, (ii) a rise in the resistivity as a function of decreasing temperature, (iii) a dip in the integrated density of states at the Fermi energy, and finally (iv) the occurrence of hybridized bands in $A(\stackrel{\ensuremath{\rightarrow}}{k},\ensuremath{\omega}).$ It is shown that in the weak-coupling limit, the charge gap of order J is formed only at ${T}_{S}$ and is hence of magnetic origin. The specific heat shows a two-peak structure. The low-temperature peak follows ${T}_{S}$ and is hence of magnetic origin. Our results are compared to various mean-field theories.

The Charged and the Spin-Excitation Gaps in the Double-Exchange Model: a Rigorous Result**The project supported by National Natural Science Foundation of China under Grant No. 19874004

We extend a previous result of ours [G.S. Tian, Phys. Rev. B58 (1998) 76121 on the charged gap and the spin-excitation gap of the half-filled Kondo lattice model to the doubleexchange model. In our original approach, this model cannot be dealt with since its localized spins have a large spin number S=3/2. By following a construction argument due to Zener and rewriting the double-exchange Hamiltonian, we are able to overcome this difficulty and re-establish the same relation for this model.

Metal–insulator transition in the half-filled Kondo lattice

The metal–insulator transition within the Kondo lattice model is studied. We show that the ground state at half-filling depends on the conduction electron dispersion relation; metallic Kondo states can be obtained. We also calculate the temperature of the metal–insulator transition; this temperature can be equal or smaller than the Kondo temperature depending on the model parameters.

Quantum Monte Carlo Simulations of the Half-Filled Two-Dimensional Kondo Lattice Model

The 2D half-filled Kondo lattice model with exchange J and nearest neighbor hopping t is considered. It is shown that this model belongs to a class of Hamiltonians for which zero-temperature auxiliary field Monte Carlo methods may be efficiently applied. We compute the staggered moment, spin and quasiparticle gaps on lattice sizes up to 12 X 12. The competition between the RKKY interaction and Kondo effect leads to a continuous quantum phase transition between antiferromagnetic and spin-gaped insulators. This transition occurs at J/t = 1.45 \pm 0.05.

The ground-state phase diagram of the one-dimensional Kondo lattice model

The periodic Anderson and Kondo lattice model describe the physics of conduction electrons in extended orbitals interacting with strongly correlated electrons in localized orbitals. These models are relevant for the so-called heavy-fermion and related systems such as the Kondo insulators. In this review we summarize recent progress in the understanding of these models, in particular, the one-dimensional Kondo lattice model. The ground-state phase diagram for the one-dimensional Kondo lattice model is determined and shows three distinct phases: a ferromagnetic metallic, an insulating spin liquid, and a paramagnetic metallic state. We present results on these phases obtained from rigorous and approximate analytical calculations supported by various extensive numerical studies on finite-size systems. The ferromagnetic phase appears in the limit of low density of conduction electrons and for strong Kondo coupling away from half filling. On the other hand, the half-filled Kondo lattice has a gap in both spin and charge excitations, i.e., it has a spin-liquid ground state. The paramagnetic phase may be considered as the generic heavy-fermion state and appears in the weak-coupling limit away from half filling. While the former two phases are well understood, the physics of the paramagnetic phase is not worked out in detail yet. In this context various questions will be considered here: Does the Fermi surface include conduction electrons only or also the localized electrons? Does the concept of Luttinger liquid apply in this case? The extension of these results to higher dimensions is also discussed. It is important to notice that the ground states of the Kondo lattice and the periodic Anderson model involve complicated effects, which cannot be understood by simple extension of the single- or two-impurity problem.

Rigorous results for half-filled Kondo lattices

It is proved that the ground state of the half-filled Kondo lattice is unique and spin singlet. For a wide class of the systems including extra interactions with various topology of the lattice structure, this proof is generalized and the total spin of the ground state is determined. A ferromagnetic ground state appears in some special cases and its criterion is given.

Spin-wave excitations of half-filled Kondo lattice model

The spin excitations in the antiferromagnetic phase of half-filled Kondo lattice model are studied by means of the decoupling approximation for spin Green's function. The spin-wave spectrum is calculated as a function of Kondo coupling, and this is used to calculate the thermodynamic quantities at low temperatures. The Néel temperature of the form T N = 0.087 J 2 ln( 1 J ) is obtained for the 3-dimensional case in the weak-coupling limit. It is pointed out that the ratio of the spin-wave velocity to the Néel temperature v s T N is enhanced as the Kondo coupling becomes small, reflecting the long-range nature of effective interactions between localized spins.

Perturbative expansions of the half-filled Kondo lattice

The Kondo lattice at half-filling has been analysed with a time-independent perturbation technique from the J → ∞ limit developed by us. We take an unrestricted tigh-binding band term. Hence, we are able to obtain results wich can be applied to different band models. In particular, we give here the ground state energy and the spin gap for the nearest-neighbours hopping band in d-dimensions.

Ground-state properties of the half-filled Kondo lattice model: A numerical study.

Ground-state properties of the one-dimensional Kondo lattice model are investigated using the quantum Monte Carlo (QMC) simulation method. To reduce the difficulty of the negative sign problem, we employ the variationally optimized singlet wave function. Since the improvement of Monte Carlo sampling efficiency is achieved in the half-filling case, we can perform the simulations on large systems (up to 26-site system). The QMC data on the local spin correlations are closely compared with those of the variational Monte Carlo (VMC) calculations as well as with the exact diagonalization data of the Ruderman-Kittel-Kasuya-Yoshida (RKKY) lattice model. We find that the local spin correlation decays exponentially with the correlation length ${\ensuremath{\xi}}_{\mathit{f}\mathit{f}}$\ensuremath{\sim}2.54 in the QMC data, while ${\ensuremath{\xi}}_{\mathit{f}\mathit{f}}$\ensuremath{\sim}1.08 in the VMC results (J/t=1). This implies the absence of the long-range order (the existence of the spin gap) and the importance of intersite correlation effects which are not taken into account in the VMC results. On the other hand, the system size dependence is almost absent in the Kondo lattice model results, which contrasts the behavior in the RKKY data.

Spin liquid ground state of the half-filled Kondo lattice in one dimension

It is shown by exact diagonalization that the one-dimensional Kondo lattice has a spin liquid ground state at half filling for all nonzero Kondo couplings. The antiferromagnetic and ferromagnetic coupling regions are characterized by the universality classes of the coherent Kondo singlet and the Haldane gap state respectively.

Spin-liquid ground state of the half-filled Kondo lattice in one dimension.

By finite-size analysis of exact diagonalization the existence of a finite spin gap is confirmed for both antiferromagnetic and ferromagnetic coupling in the half-filled Kondo lattice model. For all finite values of antiferromagnetic coupling the system belongs to a class of coherent Kondo spin singlet, whereas for any finite ferromagnetic coupling it scales to a spin S=1 antiferromagnetic chain with a Haldane gap.