Multi-Channel Kondo Model & Kitaev Quantum Quench

Abstract

This thesis consists of two parts. In part one we discuss the Kondo model. First we point out the differences in physical properties between the one- and multi-channel Kondo model using a renormalization group analysis. We also point out the challenges in obtaining exact solutions. Then we give an overview of two approaches, bosonization and spin chain, for finding exact solution of the one-, two- and four-channel Kondo model. Using bosonization we review a mapping from the one- and two-channel model to the exactly solvable resonant level model for a specific coupling strength. Following previous work, we derive the Kondo effect for a spin chain construction with XX and Ising coupling, showing the low energy behavior to be equivalent to the two- or four-channel Kondo model. We also discuss why one, two and four channels are special and we point out the difficulties in extending these approaches to other multi-channel Kondo models. Then in part two we investigate survival of the topological edge effects of the Kitaev chain (Majorana edge modes) after a quantum quench. We determine a stability region for the edge modes after chemical potential and superconductivity quenches, by analyzing the wave functions using two measure: inverse participation ratio and overlap. We see that this region does not cover the full topological phase in parameter space. The Majoranas already disappear before the quenched system has reached the phase transition.