Quantum Impurity Problems in Condensed Matter Physics

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.

Lecture Notes, Les Houches, 2008, 44 pages. Typos fixed and a new reference

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• Spatiotemporal buildup of the Kondo screening cloud
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• Holographic Kondo Model in Various Dimensions
• Competing Boundary Interactions in a Josephson Junction Network with an Impurity
• Thermodynamics of the Topological Kondo Model
• Enhanced Coherence of a Quantum Doublet Coupled to Tomonaga-Luttinger Liquid Leads
• Universal Behavior of Entanglement in 2D Quantum Critical Dimer Models
• Pairing of Cooper pairs in a Josephson junction network containing an impurity
• Quantum Fields on Star Graphs with Bound States at the Vertex
• Exact solution of the anisotropic special transition in the O(n) model in 2D
• Zeno crossovers in the entanglement speed of spin chains with noisy impurities
• Entanglement entropy scaling in solid-state spin arrays via capacitance measurements
• ABCD of Kondo effect
• Variational cluster approach to the single impurity Anderson model
• Consistent bosonization-debosonization I: A resolution of the non-equilibrium transport puzzle
• Current Reflection and Transmission at Conformal Defects: Applying BCFT to Transport Process
• On conjectured local generalizations of anisotropic scale invariance and their implications
• Nonequilibrium Quantum Critical Steady State: Transport Through a Dissipative Resonant Level
• Quantum Impurity in Luttinger Liquid: Universal Conductance with Entanglement Renormalization
• Fidelities in the spin-boson model
• Entanglement flow in the Kane-Fisher quantum impurity problem
• Anisotropic Kondo line defect and ODE/IM correspondence
• Boundary critical phenomena in the quantum Ashkin-Teller model