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.
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.
Materials classified as strongly-correlated systems often exhibit complex and fascinating properties due to interactions among electrons as well as between electrons and other constituents of the material. A common model to describe electronic system with strong on-site Coulomb interaction is Hubbard model. One very powerful approximation method for solving Hubbard model having been widely used over the last few decades is dynamical mean-field theory (DMFT). This method maps the original lattice problem into an impurity problem embedded in a self-consistent bath. Apart from the many variants of implementation of DMFT, it relies on using an impurity solver as part of its algorithm. In this work, rather than solving a Hubbard model, we propose to explore the impurity solver itself for solving a problem of metallic host doped with correlated elements, commonly referred to as Anderson impurity model (AIM). We solve the model using the distributional exact diagonalisation method. Our particular aim is to show how the metal-insulator transition (MIT) occurs in the system and how the phenomenon reflects in its optical conductivity for various model parameters.