Quantum Impurity Problems in Condensed Matter Physics

TL;DR

This paper reviews the application of Boundary Conformal Field Theory to quantum impurity problems in condensed matter, covering models like Kondo, quantum dots, and impurities in Luttinger liquids, with emphasis on theoretical frameworks and experimental relevance.

Contribution

It provides a comprehensive review of BCFT methods applied to various quantum impurity models, highlighting recent developments and their experimental implications.

Findings

BCFT effectively describes quantum impurity interactions.

Multi-channel Kondo models reveal complex impurity behaviors.

Impurity entanglement entropy offers insights into quantum correlations.

Abstract

Impurities are ubiquitous in condensed matter. Boundary Conformal Field Theory (BCFT) provides a powerful method to study a localized quantum impurity interacting with a gapless continuum of excitations. The results can also be implied to nanoscopic devices like quantum dots. In these lecture notes, I review this field, including the following topics: I. General Renormalization Group (RG) framework for quantum impurity problems: example of simplest Kondo model II. Multi-channel Kondo model III. Quantum Dots: experimental realizations of one and two channel Kondo models IV. Impurities in Luttinger liquids: point contact in a quantum wire V. Quantum impurity entanglement entropy VI. Y-junctions of Luttinger liquids VII. Boundary condition changing operators and the X-ray edge problem.