Thermodynamics and Screening in the Ising–Kondo Model

Abstract

A simplification of the symmetric single‐impurity Kondo model is introduced and studied. In the Ising–Kondo model, host electrons scatter off a single magnetic impurity at the origin whose spin orientation is dynamically conserved. This reduces the problem to potential scattering of spinless fermions that can be solved exactly using the equation‐of‐motion technique. The Ising–Kondo model provides an example for static screening. At low temperatures, the thermodynamics at finite magnetic fields resembles that of a free spin‐1/2 in a reduced external field. Alternatively, the Curie law is interpreted in terms of an antiferromagnetically screened effective spin. The spin correlations decay algebraically to zero in the ground state and display commensurate Friedel oscillations. In contrast to the symmetric Kondo model, the impurity spin is not completely screened, i.e., the screening cloud contains less than a spin‐1/2 electron. At finite temperatures and weak interactions, the spin correlations decay to zero exponentially with correlation length ξ(T) = 1/(2πT).

Second Wilson number from third-order perturbation theory for the symmetric single-impurity Kondo model at low temperatures

“…in agreement with the analytical solution in [13], see also equation (S342) of the supplemental material.…”

“…Note that V z 2 is the second-order Ising-Kondo contribution to the single-impurity Kondo model, see [13]. In section SM I of the supplemental material, we explicitly calculate the exact result of the free energy of the Ising-Kondo model for a constant density of states, see equation (13). In this way, we can compare the results from perturbation theory of appendix A with those from the Taylor series of the exact result.…”

“…To make progress, we define Following Bauerbach et al [13], we derive the free energy of the Ising-Kondo model for a constant density of states using the equation-of-motion method. Since we have explicitly performed the second-order perturbation theory for the Ising-Kondo model, see appendix A.1, we can directly compare the Taylor series of the exact result with perturbation theory.…”

“…(2024) 043102 variational wave functions, and numerical approaches such as the density-matrix renormalization group (DMRG) and the NRG methods. Also in the year 2020, Bauerbach et al [13] introduced a simplification of the Kondo model, the so-called Ising-Kondo model, in which the spin-exchange term of the full Kondo Hamiltonian is neglected. Thereby, the complexity of the Kondo model is reduced to that of potential scattering of spinless fermions, which can be solved analytically using the equation of motion method.…”