Half-filled Kondo lattice on the honeycomb lattice

The unique linear density of state around the Dirac points for the honeycomb lattice brings much novel features in strongly correlated models. Here we study the ground-state phase diagram of the Kondo lattice model on the honeycomb lattice at half-filling by using an extended mean-field theory. By treating magnetic interaction and Kondo screening on an equal footing, it is found that besides a trivial discontinuous first-order quantum phase transition between well-defined Kondo insulator and antiferromagnetic insulating state, there can exist a wide coexistence region with both Kondo screening and antiferromagnetic orders in the intermediate coupling regime. In addition, the stability of Kondo insulator requires a minimum strength of the Kondo coupling. These features are attributed to the linear density of state, which are absent in the square lattice. Furthermore, fluctuation effect beyond the mean-field decoupling is analyzed and the corresponding antiferromagnetic spin-density-wave transition falls into the O(3) universal class. Comparatively, we also discuss the Kondo necklace and the Kane-Mele-Kondo (KMK) lattice models on the same lattice. Interestingly, it is found that the topological insulating state is unstable to the usual antiferromagnetic ordered states at half-filling for the KMK model. The present work may be helpful for further study on the interplay between conduction electrons and the densely localized spins on the honeycomb lattice.     

Correlated disorder in a Kondo lattice

Motivated by recent experiments on Yb-doped CeCoIn5, we study the effect of correlated disorder in a Kondo lattice. Correlations between the impurities are considered at the two-particle level. We use a mean-field theory approximation for the Anderson lattice model to calculate how the emergence of coherence in the Kondo lattice is impacted by correlations between impurities. We show that the rate at which disorder suppresses coherence temperature depends on the length of the impurity correlations. As the impurity concentration increases, we generally find that the suppression of coherence temperature is significantly reduced. The results are discussed in the context of available experimental data.     

Spin-density wave in a Kondo lattice

An Anderson model with N-fold degeneracy in the Kondo regime is considered. It is presumed that the electron-electron correlations in the system of f electrons have their maximum strength. A criterion for instability against the formation of a weakly antiferromagnetic phase superposed on the Kondo state is obtained by the auxiliary-boson method using the 1/N expansion. An effective interaction leading to the formation of magnetic ordering appears because of the spin fluctuations in the system of localized electrons. The phase diagram of the system is constructed. Zh. éksp. Teor. Fiz. 111, 600–614 (February 1997)     

Blume-Emery-Griffiths model on the honeycomb lattice

Exact results are obtained for a spin-1 system on the honeycomb lattice with the Blume-Emery-Griffiths Hamiltonian –/kT =J _i,j S _i S _j +Ki,jS _i ² _j ² – _i S _i ² +HS _i subject to the constraintK=–ln coshJ. ForJ>0, the system behaves like a spin-1/2 Ising ferromagnet with the free energy analytic everywhere except at the first-order phase boundaryH=0, tanhJ<(2+e )/ . Derivatives of the free energy across this boundary are discontinuous and we obtain the exact expression for the spontaneous magnetization. ForJ<0, the system can be transcribed into an antiferromagnetic spin-1/2 Ising model in a real magnetic field, and from this equivalence portions of the exact phase boundary are determined.     

Diagonal composite order in a two-channel Kondo lattice

A novel type of symmetry breaking is reported for the two-channel Kondo lattice where conduction electrons have spin and orbital (channel) degrees of freedom. Using the continuous-time quantum Monte?Carlo and the dynamical mean-field theory, a spontaneous breaking of the orbital symmetry is observed. The tiny breakdown of orbital occupation number, however, vanishes if the conduction electrons have the particle-hole symmetry. The proper order parameter instead is identified as a composite quantity representing the orbital-selective Kondo effect. The single-particle spectrum of the selected orbital shows insulating property, while the other orbital behaves as a Fermi liquid. This composite order is the first example of odd-frequency order other than off-diagonal order (superconductivity), and is a candidate of hidden order in f-electron systems.     

Mott-Hubbard transition and antiferromagnetism on the honeycomb lattice

The Hubbard model is investigated for a halffilled honeycomb lattice, using a variational method. Two trial wave functions are introduced, the Gutzwiller wave function, well suited for describing the “metallic” phase at small U and a complementary wave function for the insulating regime at large values of U. The comparison of the two variational ground states at the mean-field level yields a Mott transition at U _c /t ≈ 5:3. In addition, a variational Monte Carlo calculation is performed in order to locate the instability of the “metallic” wave function with respect to antiferromagnetism. The critical value U _m/t ≈ 3:7 obtained in this way is considered to be a lower bound for the true critical point for antiferromagnetism, whereas there are good arguments that the mean-field value U _c/t ≈ 5:3 represents an upper bound for the Mott transition. Therefore the “metal”- insulator transition for the honeycomb lattice may indeed be simultaneously driven by the antiferromagnetic instability and the Mott phenomenon.     

Interactions and phase transitions on graphene's honeycomb lattice

The low-energy theory of interacting electrons on graphene's two-dimensional honeycomb lattice is derived and discussed. In particular, the Hubbard model in the large-N limit is shown to have a semimetal-antiferromagnetic insulator quantum critical point in the universality class of the Gross-Neveu model. The same equivalence is conjectured to hold in the physical case N=2, and its consequences for various physical quantities are examined. The effects of the long-range Coulomb interaction and the magnetic field are discussed.     

Exact solution of a three-component system on the honeycomb lattice

A model three-component system is considered in which the bonds of a honeycomb lattice are covered by rodlike molecules of typesAA, BB, andAB. The ends of molecules near a common lattice site interact with energies _AA, _BB, and _AB. The model is equivalent to an Ising model on the 3–12 lattice. Exact results are obtained for the two-phase coexistence curves in the isothermal composition plane.     

Topological states in the Hofstadter model on a honeycomb lattice

We provide a detailed analysis of a topological structure of a fermion spectrum in the Hofstadter model with different hopping integrals along the $x,y,z$-links ($t_x=t,t_y=t_z=1$), defined on a honeycomb lattice. We have shown that the chiral gapless edge modes are described in the framework of the generalized Kitaev chain formalism, which makes it possible to calculate the Hall conductance of subbands for different filling and an arbitrary magnetic flux ϕ. At half-filling the gap in the center of the fermion spectrum opens for $t>t_c=2^{\varphi }$, a quantum phase transition in the 2D-topological insulator state is realized at $t_c$. The phase state is characterized by zero energy Majorana states localized at the boundaries. Taking into account the on-site Coulomb repulsion U (where $U<<1$), the criterion for the stability of a topological insulator state is calculated at $t<<1$, $t\sim U$. Thus, in the case of $U>4\mathrm{\Delta }$, the topological insulator state, which is determined by chiral gapless edge modes in the gap Δ, is destroyed.     

BCS-BEC crossover on the two-dimensional honeycomb lattice

The attractive Hubbard model on the honeycomb lattice exhibits, at half filling, a quantum critical point between a semimetal with massless Dirac fermions and an s-wave superconductor (SC). We study the BCS-BEC crossover in this model away from half filling at zero temperature and show that the appropriately defined crossover line (in the interaction-density plane) passes through the quantum critical point at half filling. For a range of densities around half filling, the "underlying Fermi surface" of the SC, defined as the momentum space locus of minimum energy quasiparticle excitations, encloses an area which changes nonmonotonically with interaction. We also study fluctuations in the SC and the semimetal, and show the emergence of an undamped Leggett mode deep in the SC. Finally, we consider possible implications for ultracold atoms in optical lattices and the high temperature SCs.     

Spin-glass transition in a Kondo lattice with quenched disorder

We use the Popov-Fedotov representation of spin operators to construct an effective action for a Kondo lattice model with quenched disorder at finite temperatures. We study the competition between the Kondo effect and frozen spin order in Ising-like spin glass. We present the derivation of new mean-field equations for the spin-glass order parameter and analyze the effects of screening of localized spins by conduction electrons on the spin-glass phase transition.     

Volume collapse in the Kondo lattice

The α-γ transition of Ce and its compounds are explained within a compressible Kondo lattice model where the variation of |J|/D with volume is taken into account. We show that, contrary to the valence change model, the Kondo contribution is sufficient to induce a first order transition at low temperature from a magnetic to a Kondo phase. The disappearance of magnetism is then related to an extremely high Kondo temperature. Applications to Ce and CeAl₂ cases are given.     

Magnetic properties of the Kondo lattice

We review the magnetic properties of the Konso lattice model using the functional integral technique: we discuss the magnetic and non-magnetic phases, and some properties of these phases. Comparison with other calculations is also made. Finally some open questions are discussed.     

Pseudogap state of two-dimensional Kondo lattice

The pseudogap behavior of spectral function A(k, ω) of charge carriers is considered in the weak doping regime for a 2D Kondo lattice with a strong spin-hole antiferromagnetic interaction. The scattering of carriers is described in terms of a local polaron according to the irreducible Green functions. The behavior of the carrier spectrum in the nodal and antinodal domains is considered. The resultant value of the pseudogap is in conformity with experimental data on photoemission with angular resolution.     

Critical behaviour of the hard-core lattice gas on the honeycomb lattice

The hard triangle lattice-gas model (lattice-gas on the honeycomb lattice with first neighbour exclusion) is studied by the phenomenological renormalization method. The critical activity is found to be z = 7.85 and the critical exponents suggest that this model belongs to the 2-D Ising universality class.     

Density waves and cooper pairing on the honeycomb lattice

Motivated by the surge in research activities on graphene, we investigate instabilities of electrons on the honeycomb lattice, interacting by onsite and nearest-neighbor terms, using a renormalization group scheme. Near half band filling, critical minimal interaction strengths are required for instabilities toward antiferromagnetic or charge-density-wave order. Away from half-filling, f-wave triplet-pairing and d + id singlet-pairing instabilities are found to emerge out of density-wave regimes.     

Coherence effects in the Kondo lattice

A simple approach to the coherence effects in the Kondo lattice is presented, using the functional integral method. We show the existence of a coherence temperature T_c smaller than T_K, below which coherence between impurities appears. The density of states is calculated in an approximation which takes into account coherent and incoherent scattering. We also show how the thermodynamic properties reflect the coherence effects.