Quantum phase transitions in impurity models and percolating lattices

This thesis investigates the influence of random disorder and dissipation on zero-temperature quantum phase transitions. Both phenomena can fundamentally change the character of the phases of a quantum many-particle system and of the transitions between them. If dissipation and disorder occur simultaneously in a system undergoing a quantum phase transition, particularly strong effects can be expected. In the first paper reproduced in this thesis, we study a single quantum rotor coupled to a sub-Ohmic dissipative bath. We find that this system undergoes a quantum phase transition from a delocalized phase to a localized phase as the dissipation strength is increased. We determine the exact critical behavior of this transition; it agrees with that of the corresponding long-range interacting classical model. Therefore, the quantum-to-classical mapping is valid for the sub-Ohmic rotor model. In the second paper, we investigate the influence of sub-Ohmic dissipation on randomly diluted quantum Ising and rotor models. We find that the zero-temperature quantum phase transition across the lattice percolation threshold separates an unusual super-paramagnetic cluster phase from an inhomogeneous ferromagnetic phase. We determine the low-temperature thermodynamic behavior in both phases, and we relate our results to the smeared transition scenario for disordered quantum phase transitions. In the last paper, the influence of Ohmic dissipation on the random transverse-field Ising chain is studied by means of large-scale Monte-Carlo simulations. Our simulations show that Ohmic dissipation destroys the infinite-randomness quantum critical point of the dissipationless system. Instead, the quantum phase transition between the paramagnetic and ferromagnetic phases is smeared, as predicted by a recent strong-disorder renormalization group approach.