Quantum phase transitions in disordered antiferromagnets

Restricted until 24 July 2009.Recently quantum phase transitions have attracted the interest of both theorists and experimentalists in condensed matter physics. Quantum magnets provide a perfect playground for studying these phase transitions since they can be triggered by many control parameters such as frustration, lattice dimerization, and magnetic field. Most previous studies have focused on the magnetic properties in pure systems. In these systems, responses to the triggering parameters are found to be uniform, leading to homogeneous phases. However little progress has been made so far on the phase transitions and properties in disordered quantum magnets because they are more complicated systems, and few theoretical tools can be applied.; In this thesis we use the stochastic series expansion quantum Monte Carlo method to study quantum phase transitions in disordered magnets. We find that disordered magnets can behave quite differently from pure systems. The system inhomogeneity can strongly affect phase transitions by changing their universality class. We also find order-disorder transitions are often accompanied by the appearance of novel quantum disordered phases, in which magnetic properties behave highly nontrivial, even singular.; In this thesis two examples are studied in great detail. The first one is the phase diagram of an inhomogeneous, bond-diluted two-dimensional antiferromagnet near the percolation threshold. We show that the magnetic transition can be tuned by the inhomogeneity of the dilution from a classical percolation to a quantum phase transition. Interestingly the quantum transition still takes the nature of a renormalized percolative transition, with continuously varying critical exponents. A gapless quantum disordered phase with no magnetic long-range order but geometric percolation is found. The low-temperature uniform susceptibility diverges as a non-universal power-law of the temperature in this phase, indicating that this is a quantum Griffiths phase. In the second example, we study field-induced quantum phase transitions in two-dimensional site-diluted coupled dimers. We find that an extremely small field drives the order-bydisordered phase into a quantum disordered disordered-free-moment phase. The agnetization curve in this phase shows a series of pseudo-plateaus, which can be explained by the highly inhomogeneous field response of the free moments. A spin-boson mapping reveals that the disordered-free-moment phase can be understood as a low-field Bose glass phase, and hence the associated phase transition is a realization of a twodimensional Bose-glass-to-disordered-free-moment transition. This is confirmed by the entire phase diagram and the study of the scaling behavior of correlation length, order parameter, and spin stiffness in the critical regime