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Large Fermi surface of the one-dimensional Kondo-lattice model
Abstract
The one-dimensional Kondo-lattice model with frustrating next-nearest-neighbor hopping has a paramagnetic ground state in the strong coupling limit. This new fixed point of the Kondo-lattice model belongs to the universality class of Luttinger liquids. The Luttinger liquid phase has a large Fermi surface whose area is determined by the total number of conduction electrons and localized spins.
Course notes for graduate students on strongly correlated models (Hubbard, Heisenberg, etc.) and matterials (cuprates, pnictides, manganites.
In spanish.
Notes on a course for graduate students on computational techniques for second-quantized models on a lattice. Exact diagonalization, including Lanczos algorithm, and quantum Monte Carlo techniques.
In spanish.
The effectiveness of the recently developed Fixed-Node Quantum Monte Carlo method for lattice fermions, developed by van Leeuwen and co-workers, is tested by applying it to the 1d Kondo lattice, an example of a one-dimensional model with a sign problem. The principles of this method and its implementation for the Kondo lattice model are discussed in detail. We compare the fixed-node upper bound for the ground-state energy at half filling with exact-diagonalization results from the literature, and determine several spin correlation functions. Our ‘best estimates’ for the ground-state correlation functions do not depend sensitively on the input trial wave function of the fixed-node projection, and are reasonably close to the exact values. We also calculate the spin gap of the model with the Fixed-Node Monte Carlo method. For this it is necessary to use a many-Slater-determinant trial state. The lowest-energy spin excitation is a running spin soliton with wave number π, in agreement with earlier calculations.
Using a canonical transformation it is possible to faithfully represent the
Kondo lattice model in terms of Majorana fermions. Studying this representation
we discovered an exact mapping between the Kondo lattice Hamiltonian and a
Hamiltonian describing three spinless fermions interacting on a lattice. We
investigate the effectiveness of this three fermion representation by
performing a zero temperature mean-field study of the phase diagram at
different couplings and fillings for the one-dimensional case, focusing on the
appearance of ferromagnetism. The solutions agree in many respects with the
known numerical and analytical results. In particular, in the ferromagnetic
region connected to the solution at zero electron density, we have a
quantitative agreement on the value of the commensurability parameter
discovered in recent DMRG (in one dimension) and DMFT (in infinite dimensions)
simulations; furthermore we provide a theoretical justification for it,
identifying a symmetry of the Hamiltonian. This ferromagnetic phase is
stabilized by the emergence of a spin-selective Kondo insulator that is
described quite conveniently by the three spinless fermions. We discovered also
a different ferromagnetic phase at high filling and low couplings. This phase
resembles the RKKY ferromagnetic phase existing at vanishing filling, but it
incorporates much more of the Kondo effect, making it energetically more
favorable than the typical spiral (spin ordered) mean field ground states. We
believe that this second phase represents a prototype for the strange
ferromagnetic tongue identified by numerical simulations inside the
paramagnetic dome. At the end of the work we also provide a discussion of
possible orders different from the ferromagnetic one. In particular at
half-filling, where we obtain as ground state at high coupling the correct
Kondo insulating state.
We study critical properties of the one-dimensional integrable Heisenberg model and supersymmetric t-J model with two-band structure. We apply conformal field theory analysis to the Bethe-ansatz solution of these models, and compute bulk susceptibilities and critical exponents. The universal formulas obtained for critical exponents can be applied to nonintegrable spin and electron models with two-band structure.
Recent developments in the theoretical investigation of the one-dimensional Kondo lattice model by using the density matrix renormalization group (DMRG) method are discussed in this review. Short summaries are given of the zero-temperature DMRG method, the finite-temperature DMRG method, and also the application of the finite-T DMRG to dynamic quantities.
Away from half-filling, the paramagnetic metallic state is shown to be a Tomonaga-Luttinger liquid with a large Fermi surface. The size of the large Fermi surface is determined by the sum of the densities of the conduction electrons and the localized spins. The correlation exponent of this metallic phase is smaller than 1/2. At half-filling the ground state is insulating. The excitation gaps are different, depending on the channels, the spin gap, the charge gap and the quasiparticle gap. The temperature dependence of the spin and charge susceptibilities and the specific heat are discussed. Particularly interesting is the temperature dependence of various excitation spectra, which indicates unusual properties for the Kondo insulators.
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.
The paramagnetic metallic phase of the one-dimensional Kondo lattice model is studied by the density matrix renormalization group method. We calculate spin excitation gap and Friedel oscillations in finite systems. The finite size corrections of the spin gap and the long-range Friedel oscillations are consistent with a Tomonaga-Luttinger liquid. The Friedel oscillations reflect the charge-charge and spin-spin correlation functions. From the period of the Friedel oscillations, it is concluded that the Fermi surface is large including both the conduction electrons and the localized spins, kF = π(1 + nc)/2 where nc is the density of conduction electrons.
A one-dimensional Hubbard model with nearest and (negative) next-nearest neighbour hopping is studied variationally. This allows to exclude saturated ferromagnetism for U < Uc. The variational boundary Uc(n) has a minimum at a “critical density” nc and diverges for n → 1.
The Lieb-Schultz-Mattis theorem for spin chains is generalized to a wide range of models of interacting electrons and localized spins on a 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 noninteracting 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.
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 CeRu2Si2 . 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 CeRu2Ge2 at a
fictitious negative pressure. Some mysteries persist as the complete
observation of the FS above the metamagnetic field HM and the detection of the
dynamical ferromagnetic fluctuation near HM. The novelty of the bilayer
ruthenate Sr3Ru2O7 is discussed by comparison. Despite differences in spin and
electronic dimensionality many common trends emerge.
We investigate a Fermi surface of the periodic Anderson model by the finite temperature quantum Monte Carlo method. Although the Luttinger sum rule predicts the system has a large Fermi surface (at T=0) that contains both conduction and f electrons, the momentum distribution function n(k) at a finite temperature shows large change at a small Fermi surface that contains only conduction electrons without f electrons. Also clear signature of the large Fermi surface is not easily observed. On the other hand, the momentum-resolved compressibility dn(k)/dμ, which reflects effects of an infinitesimal doping, shows a peak structure at the large Fermi surface even at an easily accessible temperature.
Recently, there has been great progress in the theoretical understanding of the Kondo lattice model which is a basic model for the heavy electron phenomena. The ground-state phase diagram of the Kondo lattice model has been completed in one dimension, where there are three different phases: the ferromagnetic metallic phase, the paramagnetic metallic one and the insulating spin liquid phase. The last one is a theoretical prototype for the Kondo insulators. The ferromagnetic metallic phase is an example of magnetic phases with reduced moment. The paramagnetic metallic phase is the region where we expect the typical heavy electron phenomena. In one dimension it belongs to the universality class of the Tomonaga-Luttinger liquids. From the period of the Friedel oscillations it is concluded that kF is determined by the density of conduction electrons and the f-spins.
The one-particle excitation spectra and the momentum distribution functions for the periodic Anderson and Kondo lattices in one and two dimensions and their dependence on the electron density are studied by using the exact diagonalization method with twisted boundary conditions on clusters with six and eight unit cells. We find the following: in the insulating state there exist more low-energy excitations than expected for a non-interacting system with the mixing gap, and in the metallic state the heavy fermion band is formed by reconstructing the low-energy excitations in the insulating state upon doping of carriers but not by simply shifting the Fermi level. As a result, the momentum distribution function has two characteristic momenta.
The zero temperature phase diagram of the ferromagnetic Kondo model in one dimension is studied using numerical techniques, especially at large Hund coupling. A robust region of fully saturated ferromagnetism (FM) is identified at all densities. Phase separation between hole-rich and hole-poor regions and a paramagnetic regime with quasilocalized holes were also observed. It is argued that these phases will also appear in two and three dimensions. Our results apply both to manganites and one-dimensional compounds such as Y2-xCaxBaNiO5. As the transition metal ion spin grows, the hole mobility rapidly decreases, explaining the differences between Cu oxides and Mn oxides.
As an extension of our previous rigorous investigation on the spin correlations in the ground states of the half-filled Hubbard model and the periodic Anderson model [G. S. Tian, Phys. Rev. B 50, 6246 (1994)], in the present paper we study the behavior of these correlation functions at finite temperature. We show rigorously that, at any T≠0, the predominant spin correlations in these systems are antiferromagnetic. Furthermore, based on this result, we also show that a quasi-one (or two)-dimensional itinerant electron ferrimagnet must have a gapless branch of ferromagnetic excitations. This conclusion is consistent with the previous results derived by the spin-wave theory.
The key parameters that characterize the long wavelength behaviour of correlation
functions, including the Fermi momenta and the correlation length, are calculated using the
transfer matrix renormalization group for the one-dimensional Kondo lattice model. The
Fermi momentum varies slowly at high temperatures, but changes sharply at low
temperatures in association with the formation of the Kondo singlets. By comparison with
the temperature dependence of the conduction electron density, we find that the long
wavelength correlations of conduction electrons are strongly affected by the localized spins
at low temperatures. At high temperatures, the conduction electrons behave as for a
system with a small Fermi surface. However, at low temperatures, the Fermi momentum
of the conduction electrons is altered by the coupling with the localized spins.
A key to understand the physics of heavy Fermion systems is the competition between the RKKY interaction and the Kondo screening
effect of magnetic moments. The Kondo lattice model is a theoretical model for which one can study the interplay. Recently
the ground state phase diagram of the one‐dimensional Kondo lattice model has been completed. After reviewing the properties
of the three phases in the phase diagram we discuss the Kondo insulator in one‐dimension with particular emphasis on the difference
between the spin excitation gap and the charge excitation gap. We argue that the Kondo insulators may be distinguished from
the ordinary band insulators by the difference between the two gaps. Another topic which is discussed in this article is the
complicated magnetic phase diagram of the low‐carrier‐density system of cerium monopnictides. We propose that the new mechanism
which exists for Kondo semimetals may be responsible for the complicated magnetic structures in these compounds.
The one dimensional Hubbard model with nearest and (negative) next-nearest neighbour hopping has been studied with the density-matrix renormalization group (DMRG) method. A large region of ferromagnetism has been found for finite density and finite on-site interaction.
It is commonly believed that strongly interacting one-dimensional Fermi systems with gapless excitations are effectively described by Luttinger liquid theory. However, when the temperature of the system is high compared to the spin energy, but small compared to the charge energy, the system becomes "spin incoherent." We present numerical evidence showing that the one-dimensional "t-J-Kondo" lattice, consisting of a t-J chain interacting with localized spins, displays all the characteristic signatures of spin-incoherent physics, but in the ground state. We argue that similar physics may be present in a wide range of strongly interacting systems.
The variational cluster approach (VCA) is applied to study spontaneous ferromagnetism in the Hubbard model at zero temperature. We discuss several technical improvements of the numerical implementation of the VCA which become necessary for studies of a ferromagnetically ordered phase, e.g. more accurate techniques to evaluate the variational ground-state energy, improved local as well as global algorithms to find stationary points, and different methods to locate the magnetic phase transition. Using the single-site VCA, i.e. the dynamical impurity approximation (DIA), the ferromagnetic phase diagram of the model in infinite dimensions is worked out. The results are compared with previous dynamical mean-field studies for benchmarking purposes. The DIA results provide a unified picture of ferromagnetism in the infinite-dimensional model by interlinking different parameter regimes that are governed by different mechanisms for ferromagnetic order. Using the DIA and the VCA, we then study ferromagnetism in one-dimensional Hubbard chains with nearest and next-nearest-neighbor hopping t2. In comparison with previous results from the density-matrix renormalization group, the phase diagram is mapped out as a function of the Hubbard-U, the electron filling and t2. The stability of the ferromagnetic ground state against local and short-range non-local quantum fluctuations is discussed. Comment: 17 pages, 15 figures
The periodic s-d or Kondo-lattice model in infinite dimensions is mapped to the s-d model. The Fermi-surface sum rule is proved with the help of the mapping: The Fermi-surface volume corresponds to the sum of the numbers of itinerant electrons and localized spins. The Fermi-surface sum rule predicts that the system with a single conduction band is a Kondo insulator for half filling. The mapped problem for the Kondo insulator is different from the Kondo problem for a single magnetic impurity in an insulator. The charge- and spin-excitation gaps of the Kondo insulator are of similar magnitude.
As a weak-coupling analogue of hole-doped S=1 Haldane systems, we study two models for coupled chains via Hund coupling; coupled Hubbard chains, and a Hubbard chain coupled with an S=1/2 Heisenberg chain. The fixed point properties of these models are investigated by using bosonization and renormalization group methods. The effect of randomness on these fixed points is also studied. It is found that the presence of the disorder parameter inherent in the Haldane state in the former model suppresses the Anderson localization for weak randomness, and stabilizes the Tomonaga-Luttinger liquid state with the spin gap. Comment: 4 pages, RevTex, 1 postscript figure (uuencoded and compressed), to appear in Phys. Rev. B
The paramagnetic metallic phase of the one-dimensional Kondo lattice model is studied by the density-matrix renormalization- group method. We observe charge and spin Friedel oscillations. They reflect the long range charge-charge and spin-spin correlation functions. The observed oscillations are consistent with a Tomonaga-Luttinger liquid. From the period of the oscillations it is concluded that the Fermi surface is large, including both the conduction electrons and the localized spins, , where is the density of conduction electrons. Comment: RevTeX, 4 pages, 4 Postscript figures, to be published in Physical review B
We show a strong indication of the existence of a large Fermi surface in
the one-dimensional Kondo-lattice model. The characteristic wave vector
of the model is found to be kF=(1+ρ)π/2, ρ being
the density of the conduction electrons. This result is at first
obtained for a variant of the model that includes an antiferromagnetic
Heisenberg interaction JH between the local moments. It is
then directly observed in the conventional Kondo lattice
(JH=0), in the narrow range of Kondo couplings where the long
distance properties of the model are numerically accessible.
In spatial dimensions d>or=2, Kondo lattice models of conduction and local moment electrons can exhibit a fractionalized, nonmagnetic state (FL(*)) with a Fermi surface of sharp electronlike quasiparticles, enclosing a volume quantized by (rho(a)-1)(mod 2), with rho(a) the mean number of all electrons per unit cell of the ground state. Such states have fractionalized excitations linked to the deconfined phase of a gauge theory. Confinement leads to a conventional Fermi liquid state, with a Fermi volume quantized by rho(a)(mod 2), and an intermediate superconducting state for the Z2 gauge case. The FL(*) state permits a second order metamagnetic transition in an applied magnetic field.
The finite-T DMRG method is applied to the one-dimensional Kondo lattice model to calculate dynamic correlation functions. Dynamic spin and charge correlations, S_f(omega), S_c(omega), and N_c(omega), and quasiparticle density of states rho(omega) are calculated in the paramagnetic metallic phase for various temperatures and hole densities. Near half filling, it is shown that a pseudogap grows in these dynamic correlation functions below the crossover temperature characterized by the spin gap at half filling. A sharp peak at omega=0 evolves at low temperatures in S_f(omega) and N_c(omega). This may be an evidence of the formation of the collective excitations, and this confirms that the metallic phase is a Tomonaga-Luttinger liquid in the low temperature limit. Comment: 5 pages, 6 Postscript figures, REVTeX
The finite-temperature density-matrix renormalization-group method is applied to the one-dimensional Kondo lattice model near half filling to study its thermodynamics. The spin and charge susceptibilities and entropy are calculated down to T=0.03t. We find two crossover temperatures near half filling. The higher crossover temperature continuously connects to the spin gap at half filling, and the susceptibilities are suppressed around this temperature. At low temperatures, the susceptibilities increase again with decreasing temperature when doping is finite. We confirm that they finally approach to the values obtained in the Tomonaga-Luttinger (TL) liquid ground state for several parameters. The crossover temperature to the TL liquid is a new energy scale determined by gapless excitations of the TL liquid. The transition from the metallic phase to the insulating phase is accompanied by the vanishing of the lower crossover temperature. Comment: 4 pages, 7 Postscript figures, REVTeX
The transport properties of the ferromagnetic Kondo lattice model in one dimension are studied via bosonization methods. The antiferromagnetic fluctuations, which normally appear because of the RKKY interactions, are explicitly taken into account as a direct exchange between the ``core'' spins. It is shown that in the paramagnetic regime with the local antiferromagnetic fluctuations, the resistivity decays exponentially as the temperature increases while in the ferromagnetic regime the system is an almost perfect conductor. %A non-perturbative description of localized spin polarons %in the paramagnetic region is obtained. The effect of a weak applied field is discussed to be reduced to the case of the ferromagnetic state leading to band splitting. The qualitative relevance of the results for the problem of the Oxide Manganites is emphasized. Comment: 4 pages, REVTex
Low-energy properties of the one-dimensional Kondo lattice model are investigated by using bosonization and renormalization group methods. The formation of the spin and charge excitation gaps at half-filling is discussed in detail both for antiferromagnetic and ferromagnetic Kondo couplings. Also, the effect of the interaction between conduction electrons on the gap formation is studied both for the Kondo insulating phase and for the Haldane gap phase. It is found that while the repulsive interaction changes the dependence of the excitation gap on the Kondo exchange coupling, the attractive interaction can drive the Kondo (or Haldane) insulating phase to a completely different phase of massless metallic states. Comment: JPSJ-style files are included
An effective Hamiltonian for the localized spins in the one-dimensional Kondo lattice model is derived via a unitary transformation involving a bosonization of delocalized conduction electrons. The effective Hamiltonian is shown to reproduce all the features of the model as identified in various numerical simulations, and provides much new information on the ferro- to paramagnetic phase transition and the paramagnetic phase. Comment: 11 pages Revtex, 1 Postscript figure. To appear in Phys. Rev. Lett
We present a simple theory for the description of the single particle excitations in the Kondo lattice model. Thereby we derive an `effective Hamiltonian' which describes the coherent propagation of single particle-like fluctuations on a strong coupling background. Even for f-electrons which are replaced by Kondo-spins, the resulting spectral function obeys the Luttinger theorem including the f-electrons, and our calculation fully reproduces the nontrivial variation of the spectral function and momentum distribution with electron density and parameter values as seen in exact diagonalization and density matrix renormalization group studies. Comment: 4 pages, Revtex, with 3 embedded eps figures. To appear in Phys. Rev. B/Rapid Communications. Hardcopies of figures (or the entire manuscript) can be obtained by e-mail request to eder@vsf1.phys.rug.nl
Conformal field theory (CFT) with the central charge c=1 is important both in the field theory and in the condensed matter physics, since it has the continuous internal symmetry (U(1) or SU(2)) and a marginal operator, and it is an effective theory of many 1D quantum spin and 1D electron systems. So it is valuable to understand how the c=1 CFT models become unstable. In this paper we discuss an instability of the c=1 CFT, that is, the transition to the ferromagnetic state. For the U(1) CFT case, we find that the spin wave velocity v and the critical dimension K behave under reasonable assumptions.
We compute the magnetic structure factor, the singlet correlation function and the momentum distribution of the one-dimensional Kondo lattice model at the density . The density matrix-renormalization group method is used. We show that in the weak-coupling regime, the ground state is paramagnetic. We argue that a Luttinger liquid description of the model in this region is consistent with our calculations . In the strong-coupling regime, the ground state becomes ferromagnetic. The conduction electrons show a spinless-fermion like behavior. Comment: 8 pages, Latex, 5 figures included, to be published in PRB (Rapid Communications)
The one-dimensional Kondo lattice model is investigated by using bosonization techniques and conformal field theory. In the half-filled band, the charge and spin gaps open for the anti-ferromagnetic Kondo coupling. Away from half-filling, the paramagnetic metallic state is characterized by the fixed point of Tomonaga-Luttinger liquid with the {\it large} Fermi surface in accordance with known results. It is suggested that as the electron density approaches half-filling, both of spin and charge susceptibilities may show a divergence property. Comment: 11 page, YITP/K-1085
We study spectral properties of quasiparticles in the Kondo lattice model in one and two dimensions including the coherent quasiparticle dispersions, their spectral weights and the full two-quasiparticle spectrum using a cluster expansion scheme. We investigate the evolution of the quasiparticle band as antiferromagnetic correlations are enhanced towards the RKKY limit of the model. In both the 1D and the 2D model we find that a repulsive interaction between quasiparticles results in a distinct antibound state above the two-quasiparticle continuum. The repulsive interaction is correlated with the emerging antiferromagnetic correlations and can therefore be associated with spin fluctuations. On the square lattice, the antibound state has an extended s-wave symmetry.
It is believed that strong ferromagnetic interactions in some solids are generated by subtle interplay between quantum many-body effects and spin-independent Coulomb interactions between electrons. It is a challenging problem to verify this scenario in the Hubbard model, which is an idealized model for strongly interacting electrons in a solid.
Nagaoka's ferromagnetism is a well-known rigorous example of ferromagnetism in the Hubbard model. It deals with the limiting situation in which there is one fewer electron than in the half-filling and the on-site Coulomb interaction is infinitely large. There are relatively new rigorous examples of ferromagnetism in Hubbard models called flat-band ferromagnetism. Flat-band ferromagnetism takes place in carefully prepared models in which the lowest bands (in the single-electron spectra) are “flat.” Usually, these two approaches are regarded as two complimentary routes to ferromagnetism in the Hubbard model.
In the present paper we describe Nagaoka's ferromagnetism and flat-band ferromagnetism in detail, giving all the necessary background as well as complete (but elementary) mathematical proofs. By studying an intermediate model called the long-range hopping model, we also demonstrate that there is indeed a deep relation between these two seemingly different approaches to ferromagnetism.
We further discuss some attempts to go beyond these approaches. We briefly discuss recent rigorous example of ferromagnetism in the Hubbard model which has neither infinitely large parameters nor completely flat bands. We give preliminary discussion regarding possible experimental realizations of the (nearly-)flat-band ferromagnetism. Finally, we focus on some theoretical attempts to understand metallic ferromagnetism. We discuss three artificial one-dimensional models in which the existence of metallic ferromagnetism can be easily proved.
We have tried to make the present paper as self-contained as possible, keeping in mind readers who are new to the field. Although the present paper is written as a review, it contains some material which appears for the first time.
It is shown that the Kondo lattice model, for any finite coupling constant J, can be obtained exactly from the periodic Anderson model in an appropriate limit. The mapping allows a direct proof of the 'large' Fermi volume for a nonmagnetic Fermi-liquid state of the Kondo lattice model. Comment: 4 pages, 0 figures
Several important generalizations of Fermi-Dirac distribution are compared to numerical and experimental results for correlated electron systems. It is found that the quantum distributions based on incomplete information hypothesis can be useful for describing this kind of systems. We show that the additive incomplete fermion distribution gives very good description of weakly correlated electrons and that the nonadditive one is suitable to very strong correlated cases. Comment: 13 pages, RevTex file, 4 ps figures. The European Physical Journal B (2002), in press
It is shown that certain analytical properties of the propagators of many-fermion systems lead rigorously to the existence of sharp discontinuities of the momentum distribution at absolute zero. This discontinuity in the momentum distribution is used to define a Fermi surface for a system of interacting fermions. It is shown that the volume of this surface in momentum space is unaffected by the interaction. The same analytic properties are shown to lead, by direct statistical mechanical arguments, to simple expressions for the low-temperature heat capacity, the spin paramagnetism, and the compressibility of the system. These expressions are very analogous to the corresponding expressions for noninteracting particles. Finally, it is shown how the whole formalism may be generalized when an external periodic potential is present (band case).
We consider a single tight-binding band of electrons interacting with localized spin-½ magnetic moments at every lattice site. We assume that in zeroth order the system is well described by noninteracting Kondo singlets, and discuss an expansion in the electron-hopping matrix element. To second order, the bandwidth is renormalized by a factor of 2, and an effective interaction between the singlets results. We discuss the properties of the model as a function of band filling, Kondo coupling, and Hubbard electron-electron interaction. In particular, we find that the system could exhibit a charge-density-wave ground state or triplet superconductivity for certain ranges of parameters.
A simple variational description is given on the nature of overlapping
Kondo clouds, which compensate the localized f-spins in the Kondo
lattice. It is shown explicitly that the f-electrons participate in
forming a ``large Fermi surface'', although they are strictly localized.
The resulting correlated Fermi liquid, i.e., heavy fermions, is examined
with the variational Monte Carlo method and is compared with the
Gutzwiller approximation. The relation to the periodic Anderson model is
also discussed in this connection.
The Kondo lattice model can be characterized by two parameters: one is the exchange coupling constant and the other is the density of conduction electrons . In the low-density limit the Kondo lattice model has a ferromagnetic ground state for any J. In one dimension one can show further that the ground state is ferromagnetic also in the strong coupling limit at any ρ, while it has a spin liquid ground state at the half-filling. The phase diagram of the Kondo lattice model in one dimension is discussed in the entire space of the parameters based on exact diagonalization.
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.
The exponent θ of the power-law anomaly for the momentum distribution in the one-dimensional repulsive Hubbard model is calculated by the Bethe ansatz method. We express the exponent of the 4kF oscillation part of the asymptotic density correlator in terms of the fractional charge of the massless holon excitation. The exponent θ is then obtained assuming the scaling law based on the Luttinger liquid nature of the system. For U→∞ and 0, the present formulation reproduces the correct values and 0, respectively, for any filling. Furthermore our results agree nicely with the Monte Carlo calculation for finite Coulomb interaction. We explicitly show that near half-filling θ takes the value close to as long as the Hubbard gap exists.
The momentum distribution function n(k) and spin-correlation function S(k) are determined for the one-dimensional large-U Hubbard model with various electron densities. The present work is featured with an application of the Bethe-ansatz wave function, which has a simple form in the large-U limit for any electron density. Namely, its charge degrees of freedom are expressed as a Slater determinant of spinless fermions, while its spin degrees of freedom are equivalent to the one-dimensional S=(1/2 Heisenberg model. The singularity of n(k) at k=kF is analyzed from the system size dependence. In addition to the kF singularity, n(k) has a weak singularity at k=3kF; however, no detectable singularity is present at 2kF, which one might expect from the spinless fermion wave function. The singularity of S(k) at 2kF is also examined in detail. It is concluded from the size dependence that, when the system is away from half-filling, the nature of the singularity at 2kF is different from that in the Heisenberg model. The results are compared with the behavior in the weak-correlation regime examined with the perturbation calculation, the prediction of g-ology, and recent Monte Carlo calculations.
Correlation effects in interacting electron systems are subject to extensive studies as a central problem in condensed matter physics. In particular deviations from Fermi-liquid behavior due to quantum fluctuations in low dimensions have attracted continuing interest. Here, exact Bethe Ansatz results on the spectrum of large but finite Hubbard chains in conjunction with methods from conformal quantum field theory can be used to obtain exact results for the asymptotic behavior of correlation functions. The authors review this method and discuss some interesting consequences of the results.
We present numerical results for the one-dimensional symmetric Kondo lattice, obtained by using a lattice-fermion Monte Carlo algorithm in conjunction with recently developed low-temperature stabilization techniques. The results are extrapolated in imaginary-time increment and lattice size to obtain controlled estimates for various quantities in the thermodynamic limit. In particular, we compare spin correlations with Ruderman-Kittel-Kasuya-Yosida predictions and two-impurity data, and note the opening of a gap as the temperature is lowered. We next discuss certain properties of the frequency-dependent conductivity, and compare ground-state results with a strong-coupling expansion. We then perform a particle-hole transformation to obtain an ‘‘attractive-J’’ lattice and discuss the existence of superconductivity in such a model. Finally, we discuss the relevance of our results to various theoretical treatments of Kondo and Anderson lattice models.
The ground state of the one-dimensional Kondo lattice model is examined in the strong-coupling regime. An effective Hamiltonian is developed to describe low-energy processes. This leads to a ferromagnetic ground state in this regime for all conduction electron densities. The spin excitations are those of a squeezed spin chain with ferromagnetic Heisenberg exchange coupling. In addition there are quasiparticle excitations, which are discussed in detail only for the case of half filling.
Spin and charge excitations in the one-dimensional periodic Anderson model at half filling are studied in the entire range of the Coulomb interaction U. It is confirmed by exact numerical diagonalization of up to eight sites that an excitation gap exists for any U. In the strong-coupling region, both the spin-excitation gap Deltas and charge-excitation gap Deltac decrease with increasing U. A finite-size scaling shows that Deltas decreases exponentially as a function of U which is consistent with the spin gap in the Kondo-lattice model. The charge gap Deltac decreases much more slowly than the spin gap. The ratio between the two gaps, R=Deltac/Deltas, increases monotonically from unity and diverges in the strong-coupling limit: it appears to be a useful quantity for measuring the strength of electron correlation in a Kondo insulator.
The phase diagram of the one-dimensional Kondo lattice is determined by numerical diagonalization of both the original and an effective Hamiltonian describing the strong-coupling limit. The ground state in the strong-coupling region is ferromagnetic for all electron concentrations away from half filling. The weak-coupling region is characterized by a paramagnetic Luttinger liquid. For the finite-size systems studied here, the dominant spin and charge correlations are at 2kF of the conduction band.
The one-dimensional Kondo-lattice model is investigated using quantum Monte Carlo and transfer-matrix techniques. In the strong-coupling region ferromagnetic ordering is found even at large band fillings. In the weak-coupling region the system shows a Ruderman-Kittel-Kasuya-Yosida-like behavior.
The long-distance decay of correlation functions in the one-dimensional Hubbard model is determined for arbitrary band filling and correlation strength, using the exact solution of Lieb and Wu. In particular, for either infinitely strong on-site repulsion U, or in the close proximity of half filling for any U, spin-spin correlations decay like cos(2kFx)x-3/2 ln1/2(x). For infinite U the results are generalized to the case of nonzero nearest-neighbor interaction. The behavior of the frequency-dependent conductivity is also discussed, in particular in the proximity of the metal-insulator transitions occurring for half and quarter filling.
We present numerical results for the thermodynamic limit of the one-dimensional symmetric Kondo lattice over the full temperature range, obtained by using a recently developed Monte Carlo technique. In particular, we compare spin correlations with RKKY predictions and two-impurity results, and note the opening of a gap as the temperature is lowered. We discuss the relevance of our results to various theoretical treatments of Kondo and Anderson lattice models.
The ground state of the Kondo-lattice model with one conduction electron is analyzed. A rigorous proof is given that this system forms an incomplete ferromagnetic order with Stot=(N-1)/2 for antiferromagnetic exchange coupling. The wave function of the ground state is derived and some of its properties are discussed.
- Tsunetsugu