Quantum phase transitions in frustrated magnetic systems

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We have started to investigate the magnetic correlations near quantum phase transitions in antiferromagnetic (AF) spin systems with competing interactions and/or geometric frustration. Three lines of approach have been and are being used to determine the phase diagram, the excitation spectrum and dynamical response functions. First we used a diagrammatic pseudofermion approximation that has been shown to give excellent results for the pure AF Heisenberg model, to explore the nature of the intermediate phase found in numerical studies to be interlaced between the AF and collinear phases of the two-dimensional J1-J2 model. In order to organize summations of infinite classes of perturbation theory in a more systematic way, we have begun to employ the functional renormalization group method. These studies will be extended to more complex interactions and to frustrated lattices. Quasi one-dimensional model systems relevant for certain spin frustrated compounds (see below) have been studied as well. Second, we have constructed spin liquid trial states with chirality correlations and fractionalized excitations for frustrated Heisenberg models. Third, we are using the density-matrix renormalization-group method as a numerical tool to provide specific benchmarks for analytical methods and as a tool to calculate the properties of more complicated models like a helical six-leg spin-2 ladder expected to describe Ca3Co2O6. Finally, we are developing a rather general new method based on Density Functional Theory using density functionals derived from exact numerical data for finite size systems.