Hyun Lee
Numerical Renormalization Group Calculations for Impurity Quantum Phase Transitions
Supervisor: Priv. Doz. Dr. Ralf Bulla [Theoretical physics III]
Date of oral examination: 01/12/2007
The thesis presents the results of the Numerical Renormalization Group (NRG) approach to three impurity models centered on the issues of impurity quantum phase transitions. The soft-gap Anderson model is one of the most well-established cases in the contexts of impurity quantum phase transitions and various analytic and numerical methods examined the physical properties of the quantum critical phase as well as the stable phases on both sides of the transition point. Our contribution is made to the former case by analyzing the NRG many-particle spectrum of critical fixed points, with which we can see how the impurity contribution of the thermodynamic quantities have fractional degrees of freedom of charge and spin. The quantum phase transition of the spin-boson model has a long history but most of achievements were reached for the ohmic dissipation. The new development of the NRG treating the bosonic degrees of freedom broadened the range of the parameter space to include the sub-ohmic case and, as a result, second order phase transitions were found for the bath exponent $0