Friedel oscillations in the one-dimensional Kondo lattice model

Shibata, Naokazu; Ueda, Kazuo; Nishino, Tomotoshi; Ishii, Chikara

doi:10.1103/physrevb.54.13495

Cited by 62 publications

(89 citation statements)

References 19 publications

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“…Figure 6 illustrates the shrinking of the hole band between localized and itinerant descriptions. Theoretical discussions can be found in the references (38)(39)(40)(41). Above T K , studies by photoemission spectroscopy (42) indicates the exclusion of the 4f electron from CeRu 2 Si 2 FS in good agreement with references (38)(39).…”

supporting

confidence: 66%

Itinerant metamagnetism of CeRu2Si2: bringing out the dead. Comparison with the new Sr3Ru2O7 case

Flouquet

Haen

Raymond

et al. 2002

Physica B: Condensed Matter

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: Focus is given on the macroscopic and microscopic experimental works realized during a decade on the clear case of itinerant metamagnetism in the heavy fermion paramagnetic compound CeRu 2 Si 2 . Emphasis is made on the feedback between the band structure, the exchange coupling and the lattice instability. Sweeps in magnetic field, pressure and temperature feel the pseudogap of this strongly correlated electronic system as well as its equivalent CeRu 2 Ge 2 at a fictitious negative pressure. Some mysteries persist as the complete observation of the FS above the metamagnetic field H M and the detection of the dynamical ferromagnetic fluctuation near H M . The novelty of the bilayer ruthenate Sr 3 Ru 2 O 7 is discussed by comparison. Despite differences in spin and electronic dimensionality many common trends emerge.The name of metamagnetism was introduced for antiferromagnetic (AF) materials where at low temperature for a critical value of the magnetic polarization i.e. of the magnetic field (H) the spin flips (1). It gives rise to a first order phase transition. It was extended to paramagnetic (Pa) systems where field reentrant ferromagnetism (F) may appear notably in itinerant magnetism (2). Finally, it was also used to describe the case of a clear crossover inside a persistent paramagnetic state between a low field paramagnetic (Pa) phase and an enhanced paramagnetic polarized (PP) phase ; the main feature is a strong positive curvature in the magnetization (M) with a marked inflection point at H = H M .In itinerant systems, it is always possible to reproduce a strong non linearity of M in H by an effective density of states ρ(E) picture with a pseudogap near the Fermi level E F (ie minimum of density of states). The magnetic field by polarizing the system, will drive ρ(E F ) to a maximum for a given value of H M ; for a symetrical case, the relative field shift of spin up and spin down density of states will reach in phase the optimal decoupling condition (3-4).With extensive studies of the tetragonal heavy fermion compound CeRu 2 Si 2 , the experimentalists succeed to realize a large variety of experiments which lead to an excellent microscopic understanding of the feedback mechanisms between electronic, magnetic and lattice instabilities (5). The combination of the growth of excellent crystals and of the possibility of easy sweep of different effects by moderate pressure (P < 10 GPa) and magnetic field (H M = 7.8 T) has permitted to reveal major effects.They stress that, under magnetic field, the system may be driven through a magnetic instability but prevented by quantum magnetic fluctuation (6). As the situation of CeRu 2 Si 2 is highly documented, it is an excellent reference for the understanding of new examples of metamagnetism recently discovered as in the bilayer ruthenate Sr 3 Ru 2 O 7 (7). Comparison will

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supporting

confidence: 66%

Itinerant metamagnetism of CeRu2Si2: bringing out the dead. Comparison with the new Sr3Ru2O7 case

Flouquet

Haen

Raymond

et al. 2002

Physica B: Condensed Matter

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“…5,6,15 Our results imply that even for PAM, this simple picture is inadequate. In particular, we see no reason why a small to large Fermi surface crossover, marked by a FM phase, should not also appear in PAM.…”

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confidence: 51%

“…1, which has proven difficult to detect with conventional ͑Abelian͒ DMRG. 16,17 Previous DMRG calculations did show a weak FM signal at nϭ0.8 and Jϭ1.6 and 1.8, 15 but the results were discarded in later papers by the same authors. 5,4 Likewise an exact diagonalization of a very small system gave FM for n FIG.…”

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confidence: 98%

Localized spin ordering in Kondo lattice models

et al. 2002

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Using a non-Abelian density matrix renormalization group method we determine the phase diagram of the Kondo lattice model in one dimension, by directly measuring the magnetization of the ground state. This allowed us to discover a second ferromagnetic phase missed in previous approaches. The phase transitions are found to be continuous. The spin-spin correlation function is studied in detail, and we determine in which regions the large and small Fermi surfaces dominate. The importance of double-exchange ordering and its competition with Kondo singlet formation is emphasized in understanding the complexity of the model.

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“…While it is possible to introduce the direct exchange J H and treat J K perturbatively [18,19,23], it is not clear whether this approach gives a correct picture for J H /J K ∼ 0. There have been some discussions [13,14,17,18,[20][21][22] concerning whether the Fermi wavevector corresponds to a large filled Fermi sea (including also the localized spins as electrons) or a small one (including only conduction electrons). In the large positive J K limit, all conduction electrons form singlets with localized spins if ν < 1.…”

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confidence: 99%

Nonperturbative Approach to Luttinger's Theorem in One Dimension

1997

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The Lieb-Schultz-Mattis theorem for spin chains is generalized to a wide range of models of interacting electrons and localized spins in one-dimensional lattice. The existence of a low-energy state is generally proved except for special commensurate fillings where a gap may occur. Moreover, the crystal momentum of the constructed low-energy state is 2kF , where kF is the Fermi momentum of the non-interacting model, corresponding to Luttinger's theorem. For the Kondo lattice model, our result implies that kF must be calculated by regarding the localized spins as additional electrons. Strongly correlated electron systems have attracted great interest. In one spatial dimension (1D), the effect of interactions is often so strong that the independent electron approximation fails even qualitatively. The bosonization approach describes a wide range of onedimensional interacting electron systems, in which the low-energy excitations are better described in terms of bosons rather than fermions. Such a phase is generally called a Tomonaga-Luttinger liquid [1]. (For reviews of bosonization, see for example [2].) There is an important parameter, the Fermi momentum k F . Although Fermi liquid theory generally breaks down in 1D due to interactions, the correlation functions still have a singular wavevector, which is a remnant of the Fermi surface of the free electrons. Low energy particle-hole like excitations still exist at the wave-vector 2k F . In the free electron model, the Fermi momentum is determined by the particle density, ν: k F = πν (or πν/2 for spinful electrons in zero magnetic field). Luttinger proved that interactions do not change the volume inside the Fermi surface, as long as the system belongs to the Fermi liquid universality class [3]. A possible one-dimensional version of Luttinger's is simply the assertion that gapless neutral excitations exist at the unrenormalized wave-vector 2k F = 2πν. This ought to imply singularities in Green's functions at the same wave-vector. It seems that the absence of a shift in k F in 1D has been assumed in most of the literature.However, since Fermi liquid theory actually breaks down, Luttinger's proof does not directly apply to the 1D problems. A proof for 1D was proposed recently [4], but only for a very simplified model with a linearized dispersion relation and without backscattering and Umklapp term. An even more difficult example is the Kondo Lattice model, in which localized spins interact with conduction electrons. The question arises whether the Fermi momentum is determined by the density of conduction electrons only or by regarding also the localized spins as electrons.In this letter, we point out that a simple but powerful theorem can be applied to a wide range of interacting electron models on 1D lattice. A low-energy excited state is explicitly constructed with a definite crystal momentum, 2k F where k F is the free electron Fermi wave-vector for the specified density, for generic values of the filling factor. The theorem gives an exact necessary condition for th...

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Friedel oscillations in the one-dimensional Kondo lattice model

Cited by 62 publications

References 19 publications

Itinerant metamagnetism of CeRu2Si2: bringing out the dead. Comparison with the new Sr3Ru2O7 case

Itinerant metamagnetism of CeRu2Si2: bringing out the dead. Comparison with the new Sr3Ru2O7 case

Localized spin ordering in Kondo lattice models

Nonperturbative Approach to Luttinger's Theorem in One Dimension

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