By means of a projector operator formalism we study the ground state properties of the Anderson Impurity Hamiltonian. The non-perturbative treatment of the model agrees with the previous one, obtained by Inagaki [Prog. Theor. Phys. 62, 1441 (1979)] by means of a perturbation expansion with respect the hybridization term. We go beyond the Inagaki's formalism to the next leading order. It provides a very accurate calculation of the energy spectrum in the total spin sector and, in particular, the ground state energy in the whole parameter space. For a one body spinless system, the dependence of the ground state energy as a function of the impurity level obtained by this procedure remarkably agrees with analytical results. For the many body case the occupancy of the impurity as a function of the parameters is studied and it agrees with the corresponding one obtained by using the Bethe ansatz and the Numerical Renormalization Group solution of the Hamiltonian. The magnetization and susceptibility of the impurity is analyzed by studying the response of the system to an external magnetic field, from which it is possible to extract the Kondo temperature. The dependence of the Kondo scale with the parameters of the model is in excellent agreement with well-known results.
An exactly solvable one-dimensional Hubbard model with a single Anderson impurity embedded at the boundary is constructed in the framework of the quantum inverse scattering method. The model is solved exactly by the nested Bethe ansatz method. We identify the boundary bound states and determine the ground state phase diagram. By analyzing the impurity contributions to the magnetization density and magnetic susceptibility, we demonstrate that a local moment is formed at the impurity site and is screened by the host electrons, consistent with Kondo physics.
We investigate the boundary effects that arise when spin-
21 impurities interact with the edges of the antiferromagnetic spin-
21 Heisenberg chain through spin exchange interactions. We consider both cases when the couplings are ferromagnetic or antiferromagnetic. We find that in the case of antiferromagnetic interaction, when the impurity coupling strength is much weaker than that in the bulk, the impurity is screened in the ground state via the Kondo effect. The Kondo phase is characterized by the Lorentzian density of states and a dynamical scale, the Kondo temperature
TK, is generated. As the impurity coupling strength increases,
TK increases until it reaches its maximum value ${T}_{0}=2\ensuremath{\pi}J$ which is the maximum energy carried by a single spinon. When the impurity coupling strength is increased further, we enter another phase, the bound mode phase, where the impurity is screened in the ground state by a single particle bound mode exponentially localized at the edge to which the impurity is coupled. We find that, in contrast to the Kondo phase, the impurity can be unscreened by unoccupying the single particle bound mode. This costs an energy
Eb that is greater than
T0. There exists a boundary eigenstate phase transition between the Kondo and the bound-mode phases, a transition which is characterized by the change in the number of towers of the Hilbert space. The transition also manifests itself in local thermodynamic quantities---local impurity density of states and the local impurity magnetization in the ground state. When the impurity coupling is ferromagnetic, the impurity is unscreened in the ground state; however, when the absolute value of the ratio of the impurity and bulk coupling strengths is greater than
54, the impurity can be screened by adding a bound mode that costs energy greater than
T0. When two impurities are considered, the phases exhibited by each impurity remain unchanged in the thermodynamic limit, but nevertheless the system exhibits a rich phase diagram.
We investigate the boundary effects that arise when spin-
21 impurities interact with the edges of the antiferromagnetic spin-
21 Heisenberg chain through spin exchange interactions. We consider both cases when the couplings are ferromagnetic or anti-ferromagnetic. We find that in the case of antiferromagnetic interaction, when the impurity coupling strength is much weaker than that in the bulk, the impurity is screened in the ground state via the Kondo effect. The Kondo phase is characterized by the Lorentzian density of states and dynamically generated Kondo temperature
TK. As the impurity coupling strength increases,
TK increases until it reaches its maximum value
T0=2πJ which is the maximum energy carried by a single spinon. When the impurity coupling strength is increased further, we enter another phase, the bound mode phase, where the impurity is screened in the ground state by a single particle bound mode exponentially localized at the edge to which the impurity is coupled. We find that the impurity can be unscreened by removing the bound mode. There exists a boundary eigenstate phase transition between the Kondo and the bound-mode phases, a transition which is characterized by the change in the number of towers of the Hilbert space. The transition also manifests itself in ground state quantities like local impurity density of states and the local impurity magnetization. When the impurity coupling is ferromagnetic, the impurity is unscreened in the ground state; however, when the absolute value of the ratio of the impurity and bulk coupling strengths is greater than
54, the impurity can be screened by adding a bound mode that costs energy greater than
T0. When two impurities are considered, the phases exhibited by each impurity remain unchanged in the thermodynamic limit, but nevertheless the system exhibits a rich phase diagram.
An impurity coupling to both spin and charge degrees of freedom is added to a periodic
t-
J chain such that its interaction with the bulk can be varied continuously without losing integrability. Ground state properties, impurity contributions to the susceptibilities and low temperature specific heat are studied as well as transport properties. The impurity phase shifts are calculated to establish the existence of an impurity bound state in the holon sector.
The Hubbard chain with a magnetic impurity of arbitrary spin
S 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
U, 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.