Quantum phase transitions in frustrated magnetic systems

Abstract

We review our recent work on quantum phase transitions in frustrated magnetic systems. In the first part a Pseudo Fermion Functional Renormalization Group (PFFRG) method is presented. By using an exact representation of spin 1/2 operators in terms of pseudofermions a quantum spin Hamiltonian may be mapped onto an interacting fermion system. For the latter an FRG treatment is employed. The results for the J1−J2 model and similar models of frustrated interaction show phase diagrams in agreement with those obtained by other methods, but give more detailed information on the nature of correlations, in particular in the non-magnetic phases. Applications of PFFRG to geometrically frustrated systems and to highly anisotropic Kitaev type models are also reported. In the second part the derivation of quantum spin models from the microscopic many-body Hamiltonian is discussed. The results for multiband systems with strong spin-orbit interaction encountered in the iridates class of compounds are shown to resolve some of the questions posed by experiment.