Quantum phase transitions in magnetic systems

Phase transitions in quantum antiferromagnets offer exciting and novel insights into the critical behavior of matter at ultra-low temperatures.;In this thesis, we apply the stochastic series expansion quantum Monte Carlo method to study the critical properties of ensembles of antiferromagnetically coupled spins subject to quantum phase transitions. The zero-temperature phase diagram, describing various phase transitions induced by an applied magnetic field, is constructed. The corresponding quantum critical points are determined to highest accuracy, allowing a conclusive interpretation of recent experimental measurements. Moreover, the scaling properties of uniform magnetization and staggered transverse magnetizationin magnetic fields are calculated, allowing the determination of the universality class of the system. The associated critical exponents are derived from Ginzburg-Landau theory as well. We find excellent agreement between the quantum Monte Carlo simulations and the analytical results, as well as previous bond-operator calculations.;Furthermore, the critical scaling exponent, which governs the power-law dependence of the transition temperature on the applied magnetic field, is extracted from the numerical data. We show that this exponent is independent of material specific inter-constituent interactions. Moreover, it converges to the value predicted for Bose-Einstein condensation of magnons. These results are of direct relevance to compounds such as TlCuCl3 and KCuCl 3, and explain the broad range of exponents reported my exponents for field-induced ordering transitions.;Finally, we introduce geometric randomness into a model of coupled dimers. The calculations show that at finite randomness, field-induced quantum phase transitions into and out of ordered Bose-Einstein condensates pass through a Bose-Glass phase. The localization of the bosons and their finite compressibility manifests this unique regime. Once delocalized, the bosons condense, and long-range order sets in. We further detect that an intermediate magnetization plateau can occur for a parameter range, in which the spins of the doped bonds become fully polarized. This rich field-dependence is expected to be experimentally observable in weakly coupled dimer compounds with small doping and negligible spin-orbit coupling or directionality effects. The calculations in this thesis cover fundamental phases and transitions between them, as they can occur in antiferromagnetic quantum spin systems.