Magnetism in the dilute Kondo lattice model

Abstract

The one-dimensional dilute Kondo lattice model is investigated by means of bosonization for different dilution patterns of the array of impurity spins. The physical picture is very different if a commensurate or incommensurate doping of the impurity spins is considered. For the commensurate case, the obtained phase diagram is vertified using a non-Abelian density-matrix renormalization-group algorithm. The paramagnetic phase widens at the expense of the ferromagnetic phase as the f spins are diluted. For the incommensurate case, short-range antiferromagnetic correlations are found to dominate at low doping, which distinguishes the dilute Kondo lattice model from the standard Kondo lattice model. DOI: 10.1103/PhysRevB.69.174425 PACS number͑s͒: 75.10.Jm, 75.40.Mg, 05.50.ϩq Heavy fermion systems have been of great theoretical interest since their discovery some 20 years ago. 1 The central problem posed by heavy fermion materials is to understand the interaction between an array of localized moments ͑gen-erally f electrons in lanthanide or actinide ions͒ and conduction electrons ͑generally s or d band͒. This situation is well described by an antiferromagnetically coupled Kondo-type model.The solution of Kondo-type models is well understood in two limiting cases; the single-impurity limit 2 which can be reduced to a one-dimensional problem and solved via Bethe ansatz, and second the Kondo lattice model ͑KLM͒, which was solved via bosonization 3 and numerous numerical approaches 4,5 in one dimension for half filling and partial conduction-band filling. For half filling the results indicate the existence of a finite spin and charge gap. Accordingly in this case the Kondo lattice model is an insulator with welldefined massive solitonic excitations of the spin sector.For partial conduction-band filling, the conduction electrons form a Luttinger liquid, with spin and charge separation. 5 The localized spins, however, exhibit ferromagnetism, due to an effective double-exchange coupling. 3,4 The double exchange is driving the system toward ferromagnetism, while the fluctuations generated by Kondo singlets compete against this tendency. As a consequence, the paramagnetic to ferromagnetic phase transition is of the quantum order-disorder type, typical to models with an effective random field. 3 However, for small Kondo coupling and close to half filling a Ruderman-Kittel-Kasuya-Yosida liquid state and polaronic regime are always present. 4 For additional properties, see earlier reviews of Ref. 6. Beyond these two solvable limits, no rigorous results exist for the intermediate cases, where the number of impurities are neither one nor equal to the number of sites. This is the focus of our study. We concentrate on the one-dimensional case, and start from the Kondo lattice limit introducing impurity spin holes, that is, we will be dealing with a dilute Kondo lattice model ͑DKLM͒:where L is the number of sites and tϾ0 is the conduction electron hopping. We measure the Kondo coupling J in units of the hopping t. We denote by ...

Delocalization effect of the Hubbard repulsion in exact terms and two dimensions

“…On this line, one observes that in both cases mentioned in the introductory part, the U driven delocalization effect emerges on the background of a macroscopic degeneracy. Indeed, in the disordered cases, the ground states are macroscopically degenerate, 7 while in the ionic Hubbard model case, the effects are observed in the neighborhood of the point where the single occupancy at one-one site of sublattices A and B has the same energy as an empty site in A and a double occupied site in B.…”

“…13,14 The PAM has been constructed to be the simplest microscopic model used to investigate the characteristic properties of heavy fermion and intermediatevalence compounds containing elements with incompletely filled f shells 13,14 and serves as well, as a test prototype two band model used in various circumstances of interest. 7,15,16 The PAM consists of strongly correlated, almost localized f electrons that experience an on-site Coulomb repulsion U Ͼ 0 and hybridize with a band of noninteracting conduction ͑d−͒ electrons. In contrast to the one-dimensional Hubbard model, PAM is not integrable even in dimension D =1.…”

“…The used technique casts the Hamiltonian in a positive semidefinite form, 13 and the fact that a such expression has the possible minimum eigenvalue zero represents the route in obtaining the exact ground states. 23 The method can be applied even in unexpected situations in the context of exact solutions, as 14 D = 3, disordered and interacting systems in 2D, 7 nonintegrable Hubbard chains in external fields, 11 or stripe, checkerboard and droplet ground states 15 in 2D. However, given by strong correlation effects not treatable mathematically up to this moment in the studied concentration region, it has not yet been applied for the PAM at finite U 0 around half-filling.…”

Exact ground states for polyphenylene type of hexagon chains

“…To deduce exact ground states in such a case one uses a technique based on positive semidefinite operator properties whose applicability does not depend on dimensionality or integrability. The procedure itself has been described previously in details in several publications [16,17], provides results even in circumstances unexpected in the context of exact solutions as systems in two [18], or three [16] dimensions, disordered systems [19] or textures [20], being also intensively tested for chain structures [17,21,22] including hexagonal type of chains as well [23,24]. Using the method, one transforms the HamiltonianĤ in positive semidefinite form (i.e.Ĥ = nP n + E g , whereP n are positive semidefinite operators, while E g is a scalar) and looks for the most general wave vector |Ψ g with the property nP n |Ψ g = 0.…”

Exact stripe, checkerboard, and droplet ground states in two dimensions

“…The fact that ground states containing intrinsic inhomogeneities can be obtained in this manner for a "non-integrable" 15 model as 2D-PAM does not come as a surprise, since the applied procedure works even in disordered case. 16 We further note that the method is described in detail in Ref. 14 and has been previously used to solve generalized PAM type models at 3 4 filling in 2D ͑Ref.…”