Thermodynamics and screening in the Ising-Kondo model

TL;DR

This paper introduces an exactly solvable Ising-Kondo model that simplifies the symmetric single-impurity Kondo problem, revealing unique static screening behavior and distinct spin correlation decay patterns.

Contribution

It presents a simplified, exactly solvable variant of the Kondo model with conserved impurity spin, providing new insights into static screening and correlation decay.

Findings

Impurity spin is not fully screened, unlike in the symmetric Kondo model.

Spin correlations decay algebraically at zero temperature and exponentially at finite temperature.

The model exhibits static screening with unique thermodynamic and correlation properties.

Abstract

We introduce and study a simplification of the symmetric single-impurity Kondo model. 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 can be 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 $\xi(T)=1/(2\pi T)$.