Scattering approach to impurity thermodynamics

TL;DR

This paper introduces a scattering approach and the Scattering Bethe-Ansatz (SBA) for quantum impurity models, enabling detailed thermodynamic and dynamical analysis beyond traditional methods.

Contribution

The paper presents the detailed development of the SBA, a generalization of Bethe-Ansatz, for describing quantum impurities and reproduces known thermodynamic results for key models.

Findings

Successfully reproduces thermodynamic results for multiple models

Enables analysis of scattering and nonequilibrium dynamics

Provides a framework for studying impurity physics beyond equilibrium

Abstract

Recently the authors developed a scattering approach that allows for a complete description of the steady-state physics of quantum-impurities in and out of equilibrium. Quantum impurities are described using scattering eigenstates defined ab initio on the open, infinite line with asymptotic boundary conditions imposed by the leads. The scattering states on the open line are constructed for integrable quantum-impurity models by means of a significant generalization of the Bethe-Ansatz which we call the Scattering Bethe-Ansatz (SBA). The purpose of the paper is to present in detail the scattering approach to quantum-impurity models and the SBA and show that they reproduce well-known thermodynamic results for several widely studied models: the Resonance Level model, Interacting Resonance Level model and the Kondo model. Though the SBA is more complex than the traditional Thermodynamic Bethe Ansatz (TBA) when applied to thermodynamical questions, the scattering approach (SBA) allows access to an array of new questions that cannot be addressed otherwise, ranging from scattering of electrons off magnetic impurities to nonequilibrium dynamics.