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arXiv:cond-mat/0007379 · Physical review. B, Condensed matter

Spinless impurities and Kondo-like behavior in strongly correlated electron systems

Satoshi Fujimoto

Published Dec 14, 2000• 12 citations
arXivHTMLPDF

Abstract

We investigate magnetic properties induced by a spinless impurity in strongly correlated electron systems, i.e., the Hubbard model in spatial dimension $D=1,2,$ and $3.$ For the one-dimensional (1D) system exploiting the Bethe ansatz exact solution we find that the spin susceptibility and the local density of states in the vicinity of a spinless impurity show divergent behaviors. The results imply that the induced local moment is not completely quenched at any finite temperatures. On the other hand, the spin lattice relaxation rate obtained by bosonization and boundary conformal field theory satisfies a relation analogous to the Korringa law, ${1/T}_{1}T\ensuremath{\sim}{\ensuremath{\chi}}^{2}.$ In the 2D and 3D systems, the analysis based upon the antiferromagnetically correlated Fermi liquid theory reveals that the antiferromagnetic spin fluctuation developed in the bulk is much suppressed in the vicinity of a spinless impurity, and thus magnetic properties are governed by the induced local moment, which leads to the Korringa law of ${1/T}_{1}.$

DOI
10.1103/physrevb.63.024406

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We investigate magnetic properties induced by a spinless impurity in strongly correlated electron systems, i.e., the Hubbard model in spatial dimension D=1,2,D=1,2,D=1,2, and 3.3.3. For the one-dimensional (1D) system exploiting the Bethe ansatz exact solution we find that the spin susceptibility and the local density of states in the vicinity of a spinless impurity show divergent behaviors. The results imply that the induced local moment is not completely quenched at any finite temperatures. On the other hand, the spin lattice relaxation rate obtained by bosonization and boundary conformal field theory satisfies a relation analogous to the Korringa law, 1/T1T\ensuremath∼\ensuremathχ2.{1/T}_{1}T\ensuremath{\sim}{\ensuremath{\chi}}^{2}.1/T1​T\ensuremath∼\ensuremathχ2. In the 2D and 3D systems, the analysis based upon the antiferromagnetically correlated Fermi liquid theory reveals that the antiferromagnetic spin fluctuation developed in the bulk is much suppressed in the vicinity of a spinless impurity, and thus magnetic properties are governed by the induced local moment, which leads to the Korringa law of 1/T1.{1/T}_{1}.1/T1​.
We investigate magnetic properties induced by a spinless impurity in strongly correlated electron systems, i.e. the Hubbard model in the spatial dimension D=1,2,D=1,2,D=1,2, and 3. For the 1D system exploiting the Bethe ansatz exact solution we find that the spin susceptibility and the local density of states in the vicinity of a spinless impurity show divergent behaviors. The results imply that the induced local moment is not completely quenched at any finite temperatures. On the other hand, the spin lattice relaxation rate obtained by bosonization and boundary conformal field theory satisfies a relation analogous to the Korringa law, 1/T1T∼χ21/T_1T \sim \chi^21/T1​T∼χ2. In the 2D and 3D systems, the analysis based upon the antiferromagnetically correlated Fermi liquid theory reveals that the antiferromagnetic spin fluctuation developed in the bulk is much suppressed in the vicinity of a spinless impurity, and thus magnetic properties are governed by the induced local moment, which leads to the Korringa law of 1/T11/T_11/T1​.
Strongly correlated electron systems show a rich variety of interesting physical phenomena. However, their theoretical description poses a highly non-trivial task, and even the simplest models cannot be solved exactly. In this thesis the intricate behavior of the single impurity Anderson model (SIAM) and the Hubbard model is investigated. The main emphasis is laid on two-particle Green functions of these systems. To this end, existing approximation schemes are extended to be capable of treating susceptibilities as well. The quality and range of applicability of these approximations is discussed in detail. The physical pictures behind the phenomena encountered in these systems are introduced. A prominent many-body effect is the emergence of temperature dependent low energy quasiparticles in both models. The occurrence of such excitations is a result of the dynamical screening of local magnetic moments, a characteristic feature of the Kondo effect. It is argued, that within the presented approximations, the low temperature phase of these models can usually be described as a Fermi liquid. As a counterexample, the Hubbard model is shown to exhibit pronounced non-Fermi liquid behavior in situations, where a van Hove singularity in the non-interacting density of states is found in the vicinity of the Fermi level. The magnetic properties of the Hubbard model are discussed in view of the two archetypical pictures of magnetism: local moment magnetism and itinerant Stoner-magnetism. Critical temperatures for antiferromagnetic, ferromagnetic and incommensurate phase transitions are calculated, and the influence of the lattice structure and frustration is examined. In strongly correlated metallic situations, the complicated competition between Kondo-screening and local moment magnetism can lead to a reentrant behavior of the N\'eel temperature. A direct signature of the Kondo effect in the Hubbard model is found in the dynamic magnetic susceptibility, where a localized collective mode emerges at very low temperatures. It is connected to the breakup of a singlet formed by the local moments with their Kondo-screening cloud, and consequently the excitation energy is of the order of the low energy scale T*.
The Hubbard chain with a magnetic impurity of arbitrary spin SSS is studied using the Bethe ansatz technique. We consider two kinds of impurities which interact with itinerant electrons on the neighboring lattice sites without destroying the integrability. The correlations in the host always induce valence fluctuations at the impurity site. For a repulsive Hubbard UUU, an impurity coupled via antiferromagnetic exchange to the host reveals magnetic properties similar to those of the ordinary Kondo effect. In contrast, a hybridization impurity (Anderson-like) embedded into the attractive Hubbard model gives rise to essentially different magnetic behavior. This difference is a consequence of the spin gap in the host.
Strongly correlated electron systems show a rich variety of astonishing physical phenomena. However, the strong interactions make the theoretical description of these systems a highly non-trivial task. Even the simplest models cannot be solved exactly, and one has to reside to approximative solutions, which often cover only certain aspects of the physics contained in these models. In recent years progress has been made in the theoretical description of correlated lattice systems through the mapping of lattice models onto effective impurity models. The most prominent example is the mapping of the Hubbard model onto an effective single impurity Anderson model (SIAM). Within this description both models feature the prominent Kondo effect, which leads to the emergence of low energy quasiparticles. The occurrence of such excitations is a result of the dynamical screening of local magnetic moments and the corresponding formation of a low temperature Fermi liquid phase. On the other hand these theories usually fail in the description of non Fermi liquid behavior, which is for example observed in the normal state of high temperature superconductors and some Heavy-Fermion systems. Strong nonlocal fluctuations drive the dynamics of these systems. In the theoretical treatment, due to the mapping of the lattice problem to an effective single impurity problem, these fluctuations are not adequately described.\\\\ In this thesis a new self-consistent approach for the inclusion of spatial correlations is presented for the Hubbard model. In contrast to existing quantum cluster theories in this field, the approach allows for the simultaneous description of short and long range pair correlations. Due to the intimate connection of this new lattice theory with the two impurity Anderson model (TIAM) a thorough numerical investigation of the TIAM is undertaken in this thesis. The competition of the Kondo effect with the RKKY interactions is studied in great detail. Furthermore two new solvers for the TIAM are introduced, which extend existing non crossing approximations for the SIAM.
Abstract We investigate the boundary phenomena that arise in a finite-size XX spin chain interacting through an XX interaction with a spin − 1 2 impurity located at its edge. Upon Jordan–Wigner transformation, the model is described by a quadratic Fermionic Hamiltonian. Our work displays, within this ostensibly simple model, the emergence of the Kondo effect, a quintessential hallmark of strongly correlated physics. We also show how the Kondo cloud shrinks and turns into a single particle bound state as the impurity coupling increases beyond a critical value. In more detail, using both Bethe Ansatz and exact diagonalization techniques, we show that the local moment of the impurity is screened by different mechanisms depending on the ratio of the boundary and bulk coupling J imp J . When the ratio falls below the critical value 2 , the impurity is screened via the Kondo effect. However, when the ratio between the coupling exceeds the critical value 2 an exponentially localized bound mode is formed at the impurity site which screens the spin of the impurity in the ground state. We show that the boundary phase transition is reflected in local ground state properties by calculating the spinon density of states, the magnetization at the impurity site in the presence of a global magnetic field, and the finite temperature susceptibility of the impurity. We find that the spinon density of states in the Kondo phase has the characteristic Lorentzian peak that moves from the Fermi level to the maximum energy of the spinon as the impurity coupling is increased and becomes a localized bound mode in the bound mode phase. Moreover, the impurity magnetization and the finite temperature impurity susceptibility behave differently in the two phases. When the boundary coupling J imp exceeds the critical value 2 J , the model is no longer boundary conformal invariant as a massive bound mode appears at the impurity site.
We report on exact results for the low-temperature thermodynamics of a spin- 12\frac{1}{2}21​ magnetic impurity coupled to a one-dimensional interacting electron system. By using boundary conformal field theory, we show that there are only two types of critical behaviors consistent with the symmetries of the problem: either a local Fermi liquid or a theory with an anomalous response identical to that recently proposed by Furusaki and Nagaosa. Suppression of backscattering off the impurity leads to the same critical properties as for the two-channel Kondo effect.