| This dissertation presents results of theoretical research on quantum phase transitions in systems where a magnetic impurity hybridizes with a fermionic host and is also coupled, via the impurity charge, to one or more bosonic modes representing dissipative environments. Two such dissipative quantum impurity models are studied using the numerical renormalization-group technique.;The charge-coupled Bose-Fermi Anderson model describes a magnetic impurity that hybridizes with conduction electrons in a metal and is also coupled to a bath of dispersive bosons. The metallic host is described by a constant density of states, while the bath is described by a spectral density proportional to os, where the value of the exponent s depends on the particular realization of the model. The following properties of the model are established: (i) As the impurity-bath coupling increases from zero at fixed impurity-band hybridization, the effective Coulomb interaction between two electrons in the impurity level is progressively renormalized from its repulsive bare value until it eventually becomes attractive. For weak hybridization, this renormalization in turn produces a crossover from a conventional, spin-sector Kondo effect to a charge Kondo effect. (ii) At particle-hole symmetry, and for sub-Ohmic bath exponents 0 < s < 1, further increase in the impurity-bath coupling results in a continuous, zero-temperature quantum phase transition to a broken-symmetry phase in which the ground-state impurity occupancy nˆd acquires an expectation value ⟨nˆd⟩ 0 ≠ 1. The response of the impurity occupancy to a locally applied electric potential features the hyperscaling of critical exponents and o/ T scaling that are expected at an interacting critical point. For the Ohmic case s = 1, the transition is instead of Kosterlitz-Thouless type. (iii) Away from particle-hole symmetry, the quantum phase transition is replaced by a smooth crossover, but signatures of the symmetric quantum critical point remain in the physical properties at elevated temperatures and/or frequencies.;In the pseudogap Anderson-Holstein model, a magnetic impurity level hybridizes with a fermionic host whose density of states vanishes as |epsilon| r at the Fermi energy (epsilon = 0) and is also coupled, via the impurity charge, to a local boson mode. We find that the pseudogap Anderson-Holstein model shows distinctive low-temperature quantum fluctuations in two regimes, depending on the strength of the impurity-boson coupling. We study two cases of band exponents: 0 < r < 1 and r = 2. (i) For 0 < r < 1, the pseudogap Anderson-Holstein model exhibits continuous quantum phase transitions with anomalous critical exponents. At fixed weak impurity-boson couplings, as the impurity-band hybridization increases from zero, transitions occur between a local-moment phase and two strong-coupling (Kondo) phases. However, at fixed strong impurity-boson couplings, increase in the impurity-band hybridization instead leads to continuous quantum phase transitions from a local-charge phase to another two strong-coupling phases. Particle-hole asymmetry in the model with weak impurity-boson couplings acts in a manner analogous to a local magnetic field applied to the model with strong impurity-boson couplings. (ii) For r = 2, the pseudogap Anderson-Holstein model can effectively describe a particular boson-coupled two-quantum-dot setup. In this case, quantum phase transitions between local spin (charge) and strong-coupling phases are manifested by peak-and-valley features in the gate-voltage (magnetic-field) dependence of the linear electrical conductance through the device. |
